He is in UK he is not. UK citizen. He has leave to remain status.
Then look up the marriage requirements in the countries you can both travel to.
As far as I'm aware the marriage requirements in Denmark are quite simple (comparable to Canada actually in many respects), but for foreigners usually a passport is required. I understand there may be paperwork that requires you to get it done in advance. You'll have to ask some local firm with experience to determine whether the refugee travel document issued by Canada is accepted. (I would
guess it is possible since they are accepting it as a travel document, but getting a firm answer may be difficult).
Note that if your UK resident partner does not have a passport, same issue may arise in Canada. Your refugee travel document issued by Canada should be acceptable here - but check in province of residence.