I checked on Andy Stewart's "A Scottish Soldier" album, Epic 19027, 1963. The authors are listed as Grant-Stewart, published by Peter Maurice Music Co. Ltd. (ASCAP) Several of the songs on the album are listed as traditional or traditional~~arranged by whoever, so I would assume that it is not a case of his taking credit for something that was not his. Though not definite on this point, the album notes would indicate that the single came out at least two years before that. It was his first single release.

Oh, and the listing says troosers, not trousers!