Buster's "adult midget voice" is a voiceover from the incomparable Mel Blanc - the voice of Bugs Bunny.
Loosely based on the vaudeville career of Buster Keaton, who both saved and outshone his mediocre performing parents. As The Three Keatons, they headlined (and slayed them) all over the U.S., including The Palace in New York. Joe Keaton was nowhere NEAR as lovable as Jack Carson.
When Barnes tells June and Joe that Buster can't be in the act in New York because of the "Gerry Society", he is referring to the informal name of the New York Society for the Prevention of Cruelty to Children. It was founded in 1874 and one of it's co-founders was Elbridge T. Gerry. As of 2017, the organization is still very much active and the state of New York has granted agents of the NYSPCC "peace officer" status - meaning they can conduct law enforcement investigations, make arrests and carry firearms if properly trained.
"Lux Radio Theater" broadcast a 60 minute radio adaptation of the movie on
May 16, 1949 with Jack Carson and Robert Alda reprising their film roles. Dorothy Lamour played Ann Sothern's role.
Jack Carson's guitar solo was dubbed by Tony Romano and his piano solo by David Klatzkin according to a contemporary source per the AFI Catalog entry on this film.