Its far from impossible. Pretty every much every other major power in East Asia had already been taken over by Europeans.
That said, for starters, the Japanese are too technologically sophisticated to conquer without some wars occuring and there are too many Japanese to make it a white settler colony dominating an enfranchised Japanese minority like New Zealand.
I think what happens depends on who takes over and when.
If the Portuguese colonize between the 1500s and 1600s, they take over through merchant concessions and attempts at Christianizing the Emperor to make him an effective puppet like they did in the Congo or other places and if they take over, there is a good chance the Dutch or British kick them out later. There will be revolts against Christianity being imposed.
If the Dutch or British take it from Portugal or do it on their own accord, the Dutch will exploit it for mercantile gain and treat the Japanese like cheap labor and the Dutch East India company will be involved. Maybe they leave some stubborn settlers behind on Hokkaido. We can call them Nipponiers.
If its the British, they don't really try to Christianize the Japanese, though the Ainu might take up Anglicanism to get back at their former oppressors, they leave some daimyo as autonomous and then Japanese people end up as a minority in other British colonies when they emigrate there as laborers or soldiers. At some point a British monarch is crowned Emperor or Empress of Japan. How that goes down with the actual Emperor, if they are not dead, is another question entirely, let alone his subjects.