Green’s Dictionary of Slang

(US hang / prison) an affected foot-dragging walk used by New York ex-convicts and their emulators in the late 1950s and early 1960s.

1964		H. Selby Jr. Last Exit to Brooklyn 11: warm clear night and they walked in small circles, dragging the right foot slowly in the hip Cocksakie [sic] shuffle, cigarettes hanging from mouths, collars of sport-shirts turned up in the back.
2004		(ref. to 1956) R. Jacoby Conversations with the Capeman 148: half slouch, half rool, it came off as a decided strut, and was known by insiders as ‘the diddy-bopper walk.’ Others called it the ‘Coxsackie shuffle’, in honor of the reformatory [...] for young delinquent men .
2014		(ref. to 1950s) J.F.Spillane Coxsackie 97: In the fifties, the ‘diddy-bopper walk’—the defiant strut of the gang member—became known on the streets of New York City as the ‘Coxsackie shuffle’ in honor of the reformatory where it was so well practiced.