Green’s Dictionary of Slang

(UK black) a pickpocket; also attrib.

1984		Smiley Culture ‘Cockney Translation’ 🎵 Cockney say tea leaf. We just say sticks man.
1999		(con. 1979–80) A. Wheatle Brixton Rock (2004) 22: He goes walking [...] wearing nutten but his sticksman coat.
2004		(con. 1970s) N. ‘Razor’ Smith A Few Kind Words and a Loaded Gun 200: The black kids stuck together. Most of them were ‘sticksmen’, pick-pockets.