Leopold Stokowski never conducted with a baton. This is the reason why Bugs Bunny, impersonating Stokowski, promptly breaks the baton before conducting, and conducts using such dramatic hand gestures.
Bugs Bunny, as the Hollywood Bowl conductor, impersonates Leopold Stokowski, who frequently conducted at the Hollywood Bowl himself in the 1930s and 1940s and did much work in Hollywood.
Giovanni Jones' singing voice remained uncredited and unknown for many years. It was since revealed to have been provided by opera singer Nicolai Shutorev. This is noted in the commentary voice-over provided on the DVD.
One of the reasons the animators likely felt a cartoon audience would recognize Bugs is masquerading as Leopold Stokowski was because Stokowski had appeared prominently in the Disney animated classic Fantasía (1940) nine years before, repeatedly interacting with Mickey Mouse as well as conducting the symphony in the film.
Disguised as a bobby-soxer, Bugs tells Jones, "Frankie and Perry just aren't in it!" Bugs is referring to popular singers of the day, Frank Sinatra and Perry Como.