In the late morning of the 29th of January, 1509, watchmen on the tower at the mouth of the Siguan River saw something peculiar - a large* ship on the horizon that wasn't of any design familiar to them. A second one soon followed. After some initial confusion, the watchmen lit a torch to try to signal to it. Quite what they were expecting nobody knows, but the crew onboard the mysterious ships maneuvered to anchor near that watchtower. The signaling attracted the attention of the chieftain of Nyrvænn, Afi Gíslason, who joined some guards to meet the ships.
Neither of the two parties were what the other expected. For the Skræligens, this was the first time seeing non-Native outsiders since the 14th century. The crew onboard were expecting to see people more similar to the natives they saw earlier on their voyage - not these Skræligens. After the two parties cautiously greeted, and a few men rowed from the ship to set foot on land, an attempt at communication began. This was a challenge - the Skræligens knew their own language, a bit of Algonquian**, and some Latin - but this was only from the church, and had drifted somewhat due to the isolation.
The voyage of Sebastian Cabot, 1508-9
Eventually after some communication in broken Latin, it turned out that these ships were an expedition led by Sebastian Cabot (Sebastiano Caboto) for King Henry VII of England, who had been searching for a Northwest Passage but was now heading south along the coast. Realizing the importance of this, the Skræligens invited them upstream to meet with the Þing in Skrælingborg. A large feast was hastily put together for the explorers, who traded knowledge and goods. Unfortunately for Sebastian Cabot, the Skræligens did not know of any Northwest Passage, just that there were "hostile natives" on the mainland and it was too dangerous for the Skræligens to explore.
This "discovery" of Skrælige still seemed useful to Cabot - a friendly settlement would be helpful to launch more expeditions from, and the tale of a "lost Viking settlement" might help secure funding for those further expeditions. In exchange for some modern steel weaponry, Skrælige would send a volunteer as an envoy to King Henry VII to prove the existence of Skrælige. Chieftain Afi's son Magnus Afisson volunteered, knowing that he would be gone for a few years. After three more nights, Cabot set off with his crew and Magnus to the southwest, and eventually back east to England.
Sebastian Cabot
Unfortunately, Sebastian Cabot returned to England slightly after the death of Henry VII in April 1509. The new king, Henry VIII, was not nearly as interested in exploring the New World, even with the tale of the "lost Viking settlement". Cabot remained employed as a cartographer of Europe, but was unable to organize another westward expedition. Not much can be confirmed about Magnus's fate afterwards - legend has it that after spending some time in Hampton Court, he traveled with Cabot to Spain, and managed to end up on a Basque fishing expedition to modern day Newfoundland. Eventually it is told that he returned to Skrælige by himself in the 1520s. While there is some evidence that this may have happened, there is nothing conclusive.
*Relative to Skræligen ships - it was a caravel.
**Generations past knew more, but the reduced native contact led to its knowledge fading somewhat.
After the visit of Sebastian Cabot, Skrælige expected more expeditions to come soon. However, King Henry VIII's lack of enthusiasm meant that the next explorer to "discover" Skrælige would be Estêvão Gomes on the 16th of February, 1524, this time working for Habsburg Emperor Charles V. Gomes's expedition was also surprised to see the Skræligens - evidently knowledge of the settlement had not spread much beyond the English crown.
Estêvão Gomes brought a rather unwelcome surprise for Skrælige as well - plague. The most significant was smallpox, which had not been present in Skrælige since at least the 11th century. (While the outbreak of disease in the 1060s was unknown, there is some evidence that it may have been a less virulent strain of smallpox.) Around two weeks after hosting Gomes and his crew, the pox began to appear. This first wave of smallpox ended up killing about 30-40% of the population.
At first, the Abenaki were able to avoid catching smallpox - without trade, any contact between them and the Skræligens was minimal, and the smallpox epidemic eventually burned out, running out of people to infect. However, unlike with Sebastian Cabot's expedition, Estêvão Gomes's led to the start of further trade - in this case with New Spain (see Southward Trade & New Port, below). This caused the second wave of smallpox to hit in 1543, further devastating Skrælige. Seeing a weakness in the Skræligen settlement of Norðstaðr, a group of Abenaki launched a raid. While it was initially successful in pushing the Skræligens back, a few of the Abenaki ended up bringing back smallpox as well. It was just as deadly for them - rough estimates place their losses at around a third of their population. While this wasn't enough to completely destroy their society, this marked the beginning of the end for an independent Abenaki culture on Skrælige. (Natives on the mainland were fortunate that the disease did not reach them yet - this would unfortunately not be true within a century.)
Now that the territories of New Spain & the Spanish West Indies were aware of the existence of Skrælige, some merchants began to venture north. Even with the devastation left by plague, the Skræligens were able to improve their quality of life. Goods that were previously unattainable due to isolation were available again, and all sorts of newer crops from Spanish territories were available as well. While this trade was not officially sanctioned, Spanish officials generally looked the other way due to its relative insignificance.
The trade was enough to justify expanded port facilities for the larger Spanish ships - unlike Skræligen ships, Spanish ones were too big to just land on shore and be carried inland. This new port (Nyjahofn) was completed by 1539, and allowed for traders to more easily load and unload their ships. Additional buildings allowed for storage of goods, as well as a marketplace for direct sale of goods to Skræligens.
With the expanded trade and devastation of smallpox, the Manntal of 1500 was absurdly outdated. An early Manntal was commissioned in 1540, and the results were as follows:
Skrælingborg: 500 (-226)
Church & Market District: 182 (-61)
Miðrway & Nyjahofn (Formerly Miðrway & Docks): 237 (-150)
Outside of the walls: 64 (-5)
Vinstrileið village: 17 (+2)
Hœgrileið village: Abandoned (-12)
Nyrvænn: 165 (-60)
Main Village: 132 (-43)
North Village: 15 (-7)
South Village: 18 (-11)
Miðrtunga: 44 (-22)
Norðstaðr (Including one household outside the village): 63 (-15)
Eirsteinn: 56 (-21)
Abenakiborg: 8 (-1)
Smarvik: 41 (-17)
Rasbeygja: 21 (-4)
Miðrsunborg: 22 (+5)
Total population of 920 (-344).
King Christian IV of Denmark & Norway, Duke of Holstein and Schleswig
Throughout the rest of the 16th Century, the population of Skrælige continued to decline due to disease. Trade helped sustain the settlements, but they certainly weren't thriving. In the meantime, knowledge of Skrælige's existence spread throughout Europe. In 1598, an expedition was sent by King Christian IV of Denmark to contact Skrælige and assert their authority over the islands. The voyage was plagued by scurvy and colder than expected temperatures, killing about a third of the crew. When they finally saw Skrælige on the 21st of May, it was a welcome relief to them all.
When the Skræligen port workers realized that these ships were no ordinary Spanish trade mission, a meeting with the Þing was quickly convened. The meeting started slowly - while the Danes and the Skræligens could somewhat understand each other's native languages, they had significantly diverged in the past centuries. The crux of the matter was this - the Danish delegation offered the protection of King Christian IV, as well as trade and investment, in exchange for swearing fealty to the king. This would mean being united with Norway, Denmark, and Iceland (as well as the Faroe Islands).
After some deliberation, the Þing agreed to swear fealty to King Christian IV. Given the devastation of the plagues, the investment from Denmark could help them recover. This did, however, mark the end of an independent Skrælige, at least for a few centuries.
Voyage of Sebastian Cabot - https://commons.wikimedia.org/wiki/File:1508_voyage.png, originally created by Evan T Jones
Plague hits Skræligens about as hard as native Americans - genetic immunity isn't really a thing. For an example of how this played out IRL, see https://en.wikipedia.org/wiki/1707-08_Iceland_smallpox_epidemic. Skræligens had the bonus of not being occupied by hostile people, which reduced the total demographic impact, but the diseases themselves were about as deadly. Skrælige was always on the periphery, and managed to avoid many common epidemics until now.
I didn't see any evidence that there was smallpox on Gomes's ship in particular, but according to https://en.wikipedia.org/wiki/Smallpox it was present on Hispaniola in 1509 and the American continent by 1520, so it's definitely feasible.