Aside from Russia, who fought and lost a war with Japan IOTL over the very matter, the following are the most likely to colonize Korea to any degree;
France:
They fought a short war with Korea IOTL, and the French were willing to colonize areas with largish populations, so that would'nt be an issue for them.
America:
Like France America got into a short shooting war with Korea in the 19th century, however it's very, very unlikely that America would try to actually colonize it, rather we'd likely try to get some legation territories (IE small cities, or part of larger ones) with the most we'd probably go after would be Jeju island.
Germany:
While Germany was late to get into the colonial game (due to Bismarcks anti-colonialism), I think it's in the realm of possibility that they could go after Korea given the right circumstances, though it's likely they'd turn most of it into a protectorate and only actually annex/turn into colonies that less populated, strategic or resource-rich areas.
Britain:
Britain really does'nt have alot of incentive to colonize Korea, since it would'nt normally be worth it, however if a situation develops where the other powers have managed to colonize/establish protectorates over Manchuria, Shandong and Japan (or Japan just does'nt like the British) then I could see them taking it to ensure they are'nt completely left out of Northern China.