While I agree that "cut your capers" has to do with dancing about, I think he means, "I dare you to come at me with your fancy footwork, [there ain't no flies on me] you won't be able to catch me with a blow - I move too fast." And "stack your duds" -- you're sure it's not "stash" as in 'store out of the way'? -- just means strip for a fight. Men often removed most of their clothing before fighting to protect it from damage; because it was warm work, unavailable as a thing for the opponent to grip, and because it's macho to fight bare chested.
Blessings,
Barbara