given Christian II's industrious nature and great connections with the Netherlands, I could see some kind of agricultural revolution kick off at one point or another.
I remember a post by @Jürgen where he stated the importance of the Rotherham plough. I would argue that such a plough can be invented in Sweden first, rather than Denmark.
Swedish agriculture had a unique characteristic: The ploughing and soil preparation had to be done in a short time period. In order to address this issue the answer was a relative high number of draught horses per hectare, especially when compared to England or France. The large number of draught animals demanded large pastures, three or even four times bigger than the cultivated land (not including fallow). So, if anybody had the incentive to develop a Rotherham plough it was the Swedes. They had both an excellent incentive and the iron deposits. A better plough that needs fewer draught animals leads to either use a part of the pasture for cattle or having a larger cultivated area. In any case you either have more cheese and meat or grain. Greater food security is the bottomline.
In the previous link I posted on clover, it stated that in a few decades after its introduction, the grain production in Denmark doubled. Moreover, the number of cattle soared. Between clover, advanced ploughs and later on potato, you have a population explosion in Scandinavia.
Christian II was determined to crush the Hansa and create a united Nordic trade company that could do business with the New Monarchies without the German intermediaries.
Is it correct to assume that Holstein is firmly under Christian's rule? If so, Christian has in his hands the arteries that give life to Lubeck: the Stecknitz Canal. Lubeck got his wealth as a trade station with its canal connection to the Elbe. Incidentally it passes through Holstein. A second canal to Hamburg was also being built around that time. If one takes or establishes a toll on the canals to the Elbe, Lubeck becomes a hostage.
I think also that the greatest leverage Lubeck held over the Scandinavian economies was the control of the Lüneburg salt trade that arrived to Lubeck through the aforementioned canal. Salt was a strategic commodity as the local diets were based upon salted fish and meat, especially in witnertime. Granted from the 16th century onwards, french salt started to be imported in increasing quantities. Regardless, Lüneburg salt was perhaps the most precious commodity in the neighborhood.
If it is alright with you all, I would like to comment also on the proto-colony established in Newfoundland/Terra Nova/ Vinland.
If I understand correctly it was established close to OTL St Johns. What a stroke of luck! This area is one of the few in the island where there is semi-decent soil for agriculture. https://www.geostrategis.com/c_cli-stjohns.htm
Moreover, the first foundry in North America was established there, as there are various iron deposits in the area, mostly bog iron. So, decent land, excellent ports, millions of cod, bog iron, lumber and a very low number of Natives. This colony is born to prosper. One should not underestimate the economic importance of cod: By the end of the 16th century more than 60% of the fish consumed in Europe was cod. A short and great reading is "Cod: A Biography of the Fish that Changed the World", by Kurlansky. By 1770 the british fisheries of New England and Newfoundland exported a surplus of 600k sterling worth of cod, when all the furs of the Hudson's bay Company were worth 9k. The New England merchants built their capital on cod.
There is a very valid argument that goes like that: "Alright you discovered the Grand Banks. Your fishing fleet visits for some months and then goes home. You need a 20/20 hindsight to establish colonies there, as they don't produce profit". A very valid argument, especially for the traditional colonizers of North America, be they English, French or Dutch. In real life, people didn't leave their comfortable lands to a new and wild land just to settle there, if there was no possibility of gold or plunder. But what about Iceland? A nation that had very little and unproductive farming land, endured climate much tougher than Newfoundland and St Lawrence, faced terrible and regular famines and was mostly cut off until the 20th century. This new land is an answer to prayers. Moreover, Iceland lacked timber and iron and paid a premium in stockfish to English traders to be provided with such vital materials. As I mentioned above, this new station in Vinland has both bog iron and timber. At that time Iceland had a population of about 30,000 ( at least I think so, perhaps a bit more). I find it very plausible to see a tickle of Icelanders migrating to the New World each year after establishing the colony. In a year of famine, I think hundreds would migrate. I think a similar pattern may be plausible for Faroe and Shetland islanders as well, in much smaller scale. So, I believe that just the Scandinavian arctic and subarctic Atlantic islands will provide a fair number of colonists, even just to avoid famine back home. In 1666, after 62 years, New France had 3,215 settlers who claimed everything north of Kennebec River in Maine. I bet Icelandic North America, with not a single settler from Norway/Denmark/Sweden, can have the same number of settlers in far less than 62 years. After all, the OTL New france population doubled every 20 years.
After the first wave of settlers succeeds, it is easy to see Norwegians and Swedes to be attracted. During the 16th century, agricultural land saw a substantial expansion in Sweden. However, land had to be cleared by dense forests in a laborious effort that took years. A new swedish farm wouldn't be able to pay any taxes for 10 to 12 years. While most of the new farmers would prefer to stay in lands close to home, I think that a minority would prefer to migrate to the New World since the effort to build a new life is pretty much the same, with more natural resources available. If the Crown sponsors a few settlers like that, I believe that there would be enough volunteers.
Last but not least, don't forget the Frisians. Centuries upon centuries Frisians had to deal with periodic overpopulation, encroachment of the North Sea and poor sandy soils. Nova Scotia happens to have saline bogs and sandy soils. Frisians would be the ideal settlers for Nova Scotia, far better acclimatized to it than the OTL French and British.
Overall, I think it is quite possible to have a Scandinavian North America of 16-20k people by 1600, before any other power gets interested in the boreal forests of the New World.