A perriwig. Rum strum: a fine large wig. (CAMBRIDGE) To do a piece. Foeminam subagitare. Cant.
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.
Strong Man * To StrumNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes