If the word doesn't ring true that wouldn't be because it would be anachronistic. The earliest use of instrument to mean musical instrument listed gin Shorter Oxford English Dictionary is 1509.

It's a different image frrom the standard line, but I'd say equally true.

It's likely enough a floating verse used or adapted by Burns, as was often his way. It'd be interesting to know if the instrument version was floating around as well, before being incorporated into that a-roving song.