I agree that song-sheets might be a bit scary for an audience unused to singing. What might be appreciated is some sort of printed handout afterwards, with either the words to the songs or some information about them, so that anyone who's interested can find out more.

Other songs you might consider are Death and the Lady, Reynardine, and the Cruel Mother. Or perhaps one of the versions of the Two Sisters that has the spooky bit about the talking bird and/or the self-playing harp made of bone. Some versions of this have repeated refrain lines that the audience might join in, but don't be put off if they don't.

Don't worry about the songs being unaccompanied. This fits very well with story telling, as it focuses the attention on the words.

Marje