I was going to look it up in a dictionary of word origens, but someone with the OED aught to handle that.

I don't hear "Scotch" being used in place of "Scot," or "Scots," over here, except in the case of "Scotch-Irish."

Usually it is "Scottish."

My family had a celebration "Scotch-Irish Day," and it was a pun on the drinking. They don't drink anymore, so now "Scotch" is a double pun; they scotched the scotch. Just in case you come across my thread on that BECAUSE I didn't point out the pun too well, and I don't think it came across as I planned. Aye, "of mice and men."