I would suggest (and don't have a clue to guide you in a search) that you check out some early Sam Levinson recordings...which are musical and also comedy based with a lot Yiddish.

My parents loved his stuff and of course it was shared with me growing up, and I guess the late Allan Sherman was sort of a successor. There is a great Allan Sherman album with a lot of Yiddish in it as well, called "Allan Sherman and His Friends - More Folk Songs".

Not even sure if either of the people, exist today on CD.