Were also the first to cut Tain't Nobody's Bizness If I Do (see there). The Shimmy was sort of a precursor of the Charleston (see there). The dance was an underground hit since the early 1910s and surfaced in the Ziegfeld Midnight Frolics of 1919 where it was demonstrated by Bee Palmer and Gilda Gray. That same year the same two introduced the Shoulder Shaker in All The Quakers Are Shoulder Shakers In Quaker Town. Fact is, Wish I Could Shimmy's basic outline was tweaked from one of Louis Armstrong's earliest compositions: a naughty piece called Take Your Feet Off Katie's Head, which he 'wrote' around 1917. New Orleans musicians had this reputation never to worry too much over song registration, copyrights, royalties and stuff, especially if they couldn't read or write. Armstrong was black as the coal he hauled, Piron was creole.
Cotton Pickers [with members of same OMF for Brunswick]
California Ramblers [also with members of OMF for Vocalion]
Eva Taylor [with her husband Clarence Williams, who published the song that same year, freed from his partner and author Armand Piron, violist, bandleader and hairdresser in New Orleans; his barbershop was a meeting place for musicians; the Williams & Piron Music Company was the first black-owned music publishing company in town]
Virginians [n°3 US]
Earl Hines [long before his partnership with Billy Eckstine]
New Orleans Feetwarmers [with Sidney Bechet]
Mary Kaye Trio [hit US]
Beatles [in Hamburg as Shimmy Shimmy]
Timebox [inspired I Wish I Could Jerk Like My Uncle Cyril]
Big Rude Jake [with Big Sugar]
I Wish I Could Shimmy Like My Sister Arthur by The Shadows only matches thematically.