IB

You may be right, of course. Certainly, the Shakespeare quotation has a singular fiddle-stick. But it's not clear from that quotation (which is the earliest recorded use in OED) that a fiddle-stick is a bow.

Other names for the sticks used to hit fiddle-strings with are straws, beating sticks, and beating straws. Usually the sticks are very light wood or (nowadays) bamboo. Knitting needles were occasionally used, but that wasn't the norm. Generally, it was an apprentice fiddler who acted as the "straw-beater," but occasionally, as you say, it was the fiddler's wife.

Is this limited to a small region of the US? I don't think so. In the Library of Congress we have examples from Mississippi and Florida, it was known on Georgia plantations in slavery times, (according to the book The Sounds of Slavery by Shane White), and it was common in Idaho at the Weiser Old-Time Fiddling contest. As you can see from the video, it's part of Cajun fiddling too. According to ethnomusicologist and fiddler Erynn Marshall, it was done up in Quebec as well. Those limits define what is really a rather vast area of North America. And the question arises: where id it come from? It could have come from Britain, or France, or been made up in the new world.

Still, of course, no one would nominate fiddlesticks as England's National Musical Instrument.

(Did you like that heroic effort to rein in thread drift?)