"Sarky" and "sarkiness" are perfectly good words. So is the variation "snarky", which is more current in the US (and, I think, Australia).
But their derivation is a bummer. I so much wanted "sarky" to be a Lowland Scots variation of "shirty", and "snarky" to be from Lewis Carroll's
The Hunting of the Snark. Contrary to my desires, the dictionaries tell me they are short forms of "sarcastic".
Nannie Dee, the original wearer of the "cutty sark" (from Burns,
Tam O'Shanter, by way of artist John Faed)