According to http://www.musiktiteldb.de/Sampler/Album1719.html Josephine Baker's precise recording date was January 12 1927.
The Clicquot Club Eskimos' version was recorded October 28 1926 - http://www.78discography.com/COL500D.htm
It looks like there is a recording from September 1926, released under the names Original Dixie Ragpickers (Grey Gull 1398) and Newport Society Orchestra (Madison 1614). Both have the matrix number 2126 so probably the same recording. Both are in 78discography.com. This looks like the first one.
Quite a few artists recorded the song in October 1926, mostly before October 28.