Ed Cray in his The Erotic Muse: American Bawdy Songs. 2nd edition has this song on page 252 with music (tune unidentified).

See here:

https://www.google.com/books/edition/The_Erotic_Muse/W8PvCRbEKLYC?hl=en&gbpv=1&dq=%22wanna+play+piano+in+a%22&pg=PA252&printsec=frontcover