Wow, that Real Audio link still works after all these years.
The Jim Kweskin Jug Band recorded a nifty cover of Ukelele Lady.
Speaking of nifty covers, I have a tattered copy of the sheet music, dated MCMXXV--a barefoot flapper on the beach with palm trees, ocean liner, and sunset in the background. Inset is a photo of two dapper vaudevillians with the legend "Featured by Correll & Gosden".

Anyway, as to the authorship of Ukelele Lady:
Words by Gus Kahn
Music by Richard A. Whiting