Despite a couple of handicaps (my name is Richard Careaga and I've been window-free for 15 years) and I don't use shiny much.
I think there are two solutions, one cumbersome and the other perhaps a long-shot.
The cumbersome approach is to use Unicode for the "special" (Anglocentrically) characters, rather than relying on encoding.
The other possibility is to save the source file with LATIN-1 or the usual encoding for Danish-language documents, rather than UTF-8. I think that will work if shiny permits.