According to the OED, 'fiddlestick' singular was in use as early as the fifteenth century (as IB says), and meant 'bow'. The record seems to show people saying "A fiddlestick's end!" (to mean 'something and nothing', 'something completely inconsequential') a bit before people were saying "Fiddlesticks!" (to mean 'nonsense'). It's not conclusive, but it looks to me as if "Fiddlesticks!" is a mutation of the earlier phrase; apart from anything else it's punchier and easier to say.