Green’s Dictionary of Slang

a measure of alcohol (leading to drunkenness).

1866		Birmingham Jrnl 3 Nov. 11/3: Until it comes to the regular toddy time, you take a ‘wee drappie,’ or a ‘thimblefull,’ or a ‘skitey’.
1914		Aberdeen Wkly Jrnl 27 Mar. 2/4: ‘Was Livingstone sober?’ ‘Witness — ‘He had a good “skitey” in [...] He was considerably under the influence of drink’.