Green’s Dictionary of Slang

crush n.3

also crusher
[note mid-19C UK SE crush hat, a soft hat that can be crushed flat, esp. a hat constructed with a spring so that it collapses and becomes flat]

(US) a hat, esp. a soft, felt one.

[UK]Bristol Magpie 1 Mar. 13/1: [A]a stout short-sighted fiend in human form [sat] dead on the cherised pericranium coverer. Alas! poor ‘tile.’ Tableau! Ten thousand apologies; and a ‘crusher’ .
[US]J. Lait ‘Omaha Slim’ in Beef, Iron and Wine (1917) 112: [He] was distinguished among the hobos because he carried a pocket comb, and, from time to time, would take off his worn and shiny crusher and caressingly comb his shock.
[US]M.H. Boulware Jive and Sl.