@gronkle I had a brief hope that there could be some common origin* and that such a meaning had been forgotten (my Swedish sources for the meaning of the word only reach back to the 16th century, so might have overlooked an earlier meaning), especially since a forgotten meaning of Sked (usually spoon) is Slida (knife sheath, but also vagina). (And since we only know Sketna Gertrud Syltekona from some judicial documents, Sketna might have been a pronounciaton typo of Skedna, as in one who has used her vagina)(*Common origin sourced from the Nordic languages, through Danish presence in Britain or Norwegians in Scotland, Ireland and Isle of Man)
Buut sadly the BE slang 'sket' is by Wiktionary supposed to be derived as a clipping from the Caribbean slang word 'skettle' with the meaning of promiscous.
Then again, the Online Etymology Dictionary has
'skit' as "piece of light satire or caricature," 1820, from earlier sense "a satirical remark or reflection" (1727), originally (1570s) "a vain, frivolous, or wanton girl" (originally Scottish, now archaic), related to verb meaning "to shy or be skittish, caper, frolic" (1610s), perhaps from Old Norse skjuta "to shoot, move quickly"
where the last meaning might have had a vovel shift to 'sket' once the humorists took over 'skit'.
tl/dr: Interesting it was. Language is weird. Historical anecdotes can be fun.
(And English language is often described with either "English is three languages stacked on top of each other wearing a trench coat" or "[English is] a language that lurks in dark alleys, beats up other languages and rifles through their pockets for spare vocabulary" - and those metaphors are not mutually exclusive.)