marlene dietrich songlist in Google produced a fairly long list of English, French and German titles, maybe not all the ones you are seeking, with limited free downloads. A thought occurred to me - if these songs have been processed for mp3 etc, they may be in a stereo format - but it would be an artificial stereo effect, so your karaoke software might still be unusable.

How about looking for cover versions by more recent artists. Even now there are quite a few singers who make a point of sticking fairly closely to Dietrich's interpretations - but you might be able to separate out the backing as you suggest. Not familiar with this field, so can't come up with any names.

Sounds like an interesting project. Good luck.

Ross