Green’s Dictionary of Slang

the injecting of a narcotic into the skin but not into a vein.

1964		Larner & Tefferteller Addict in the Street (1966) 25: I wasn’t shooting it up, I was just skinning it then. Skinning is just where you hit anywhere in your body and shoot the dope in. That’s with heroin.
1969		R.R. Lingeman Drugs from A to Z (1970).