circuit in Chicago, they created a tap dance routine they called "Goofus"[3] to the tune Turkey in the Straw.
[1] At the end of many performances, all of the musicians, singers, and dancers would get together on stage and do one last routine: the Shim Sham Shimmy.
[7] At the Savoy Ballroom, some lindy hoppers did the shim sham as a group line dance, without the taps.
An obvious choice is The Shim Sham Song (Bill Elliot Swing Orchestra), which was written specifically for this dance and has musical effects (e.g., breaks) in all the right places.
However, today the Shim Sham — particularly the Frankie Manning version — is danced more often to "'Tain't What You Do (It's The Way That Cha Do It)" by Jimmie Lunceford and His Orchestra, or "Tuxedo Junction" by Erskine Hawkins.
In fact, it is typical now at a Lindy dance party for dancers to start up a Shim Sham whenever "'Tain't What You Do" is played.