I think that if you’re looking at the issue from the perspective of sovereignty recognized by the international community, which seems to be the question raised by the OP, then none of the British dominions would be considered independent in 1900.
This was illustrated most glaringly when the British government declared war on Imperial Germany in 1914 - all of the British dominions were automatically at war, without any choice on their part. As well, they couldn’t sign international treaties on their own behalf, but had to go through the U.K. government.
This changed after WWI. All of the dominions signed to Treaty of Versailles seperately instead of a single imperial signature. Each dominion was also accorded it’s own membership in the League of Nations. Mostly this meant that each dominion’s High Commisioner in London became it’s Ambassador to the LoN.
The Guinness list seems to be limited to the nations in existence as separate and independent at the time it was compiled in 1976, and doesn’t include any that may have been such in 1900 but have changed status since, such as the various bits of what was then Yugoslavia.
I was thinking about the islands of the pacific. Many had independence that flipped quite a bit. For instance according to a wikipedia article Tonga was an independant country then lost its independence during the year 1900.
Depending oh how far around 1900 you’re talking about a few more should show up.
This should be either 301 or 1291, depending on your criteria for independence. I doubt that the treaty of 1631 had any substantial impact on sovereignty, but I can’t find a detailed summary online.