One common variant is fiddlestick's end. Literally, a fiddlestick is a bow used to play a fiddle. There is nothing at either end of the bow, which ends at a point. It seems that "fiddlestick's end," meaning "nothing," could be part of the story of how "fiddlestick" came to mean "nonsense."
The entry in Green's Dictionary of Slang seems to me to suggest as much:
fiddlestick’s end (n.) a [Standard English] fiddlestick ends in a point.
[late 18C–1900s] nothing; thus as excl., a dismissive retort.
OED also suggests that the meaning lies somewhere between absurdity and "nothing."
- humorously. Something insignificant or absurd, a mere nothing. Often substituted for another word in derisively repeating a remark. Also, fiddlestick's end. not to care a fiddlestick: to care not at all.
A few citations:
1796 Grose's Classical Dict. Vulgar Tongue (ed. 3) Fiddlestick's End, Nothing.
1807 Salmagundi 18 Apr. 161 We do not care a fiddle~stick..for either public opinion or private ill-will.
1839 Dickens Nicholas Nickleby viii. 65 ‘We purify the boys' bloods now and then...’ ‘Purify fiddlesticks' ends’, said his lady.
This might not be the complete story, but it could offer a hint as to how fiddlestick came to mean "nonsense" or "absurdity."
