To wipe, or slap. Snite his snitch; wipe his nose, i.e. give him a good knock.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Snitch * To SnivelNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes