Instrument credits are believed to be:
Vocals - Stan Freberg (credited on the short)
Saxophone - Pepper Adams (or possibly Jimmy Giuffre)
Trumpet/flugelhorn - Shorty Rogers (credited on the short)
Piano - Pete Jolly
Guitar - Barney Kessel
Bass - Red Callender (or possibly Red Mitchell)
Drums - Stan Levey (or possibly Shelly Manne)