Green’s Dictionary of Slang

to perform menial tasks; thus skivvying n.

1929		(con. 1916) F. Manning Her Privates We (1986) 44: What these luxurious creatures really wanted was a man to skivvy for them.
1939		‘Flann O’Brien’ At Swim-Two-Birds 74: Little black maids skivvying there in the galley.
1943		Western Times 26 Mar. 7/5: The W.A.A.F. [...] refused to ‘skivvy’ at an R.A.F. officer’s private house.
1968		Punch 21 Feb. 287: There are now better jobs than skivvying to look for.
1986		(con. 1920s) P. Barker Liza’s England (1996) 34: You’re supposed to skivvy after ’em and get it all done and out of the way while they’re flat on their backs.
1999		Guardian Sat. Rev. 26 June 2: That bloke with the bouffant hairdo who used to skivvy for Harrods.