In reply to:

But it derives through Spanish from picar, to prick. AHD lists piccolo as of obscure origin.

Well, then, the prick/piccolo connection could be the pricking effect of the sound itself. Very different from the flute, I think. Think of "Stars and Stripes Forever"--the little piccolo solo that pricks the air with bursts of aural pinpoint notes. I suppose we could call the piccolo the prickolo... Sounds like the perfect instrument for a nit-picker.