Herringbone which starred the late David Rounds in the late 70s or early 80s, had one actor. I didn't see it and I don't think it was recorded. This was performed at Playwrights Horizon or some NYC company.
Songs From an Unmade Bed also uses but one actor and was done about 5 years ago at the NY Theater Workshop. This was not a musical per se, but a song cycle. There is a recording of this show.
A chorus can be as small as you can get away with. I have seen productions of High Spirits and Do I Hear a Waltz? that cut the chorus entirely.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher