A recording is featured on the album:
Gershwin: The 1920s & The 1930s
Track 8: PROMENADE (Walking the Dog) (2'55")
written for the film "Shall We Dance"
Los Angeles Philharmonic - Michael Tilson Thomas
released on the CBS Masterworks label (MK 39699)

My copy of the CD dates from 1986 and the sleeve notes state this was the premiere recording of this 1936 composition.

Hope these notes are of use.

Mitch, February 1, 2007; 8:09 AM