A hand or foot; look at his dirty paws. Fore paw; the hand. Hind paw; the foot. To paw; to touch or handle clumsily.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
See also the definition in Nathan Bailey's 1736 dictionary of canting and thieving slang.
Paunch * Paw Paw TricksNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes