Green’s Dictionary of Slang

1. (US) a skull-cap.

1938		News-Palladium (Benton Harbor, MI) 3 May 8/7: [advert] Free — Baseball Caps for Boys. Skully Caps for Girls.
1992		Apache ‘Tonto’ 🎵 My dick so big, I use a skully for a jimmy hat.
2006		G. Pelecanos Night Gardener 198: Toby was topped by a black skully and both wore their jeans low.
2012		Future ‘Blow’ 🎵 Put the Gucci skully on.

2. see skull n.¹ (9)