France, Spain, Russia. Russia and Denmark had...somewhat amicable relations if memory serves, and Russia wouldn't mind a credible western counter-balance to Sweden.
I don't see France and Spain being much exited about the prospect, though.
Also, there is the matter of religion: Though both Denmark-Norway and England was non-RC, they were different branches of non-RC: Denmark-Norway was solidly Lutheran, and England Anglican. There's going to be some difficult theological conversations there...