I have a CD of 1930's silliness that has Leslie Holmes (who teamed up with the incomparable Leslie Sarony as The Two Leslies) singing "What Can You Give a Nudist for His Birthday?".

It's the same song as Gracie's but with gender references relevant to a lady nudist, and a good deal of patter between verses.

I shall look it out and transcribe it, but it might be a while yet.

LFF