Two thoughts - The Stewart mentioned earlier was Davy Stewart, who did indeed accompany himself on the accordian. He was also a piper and it has been said that his very strange chording on the accordian was because of that background. His accompaniment of singing may have been because his usual audiences (cinema queues and the like) would expect that. It's worth hearing his version of 'MacPherson's Rant'.
and - Tom Speirs (lately of 'The Gaugers), although not a 'source' singer stays very close to his Aberdeenshire traditions and he accompanies himself on the fiddle.