If it's any comfort, "dese", "dem", and whatever really just correspond to real pronunciation-- people still say "gwine" all the time, just because that's the way they pronounce the word, so don't worry too much about that. An' dey'ze whaht folks! Sho nuff!

As to the songs themselves, it is possible to pick out songs that don't have offensive references in them. And, of course, a lot of songs that originally had offensive references in them have been tidied up, and you can find lyrics to everything on line nowadays.

Stay away from the face painting and the minstrel show characters, and it can work.

By the way, you do realize that "fifty years ago" was 1958--when the big hits were "At the Hop", "All I have to Do is Dream", "To Know Him is to Love Him", and "The Chipmunk Song", don't you? It takes a while to get used to it;-)