I enquired about the left handed salute and was fortunate enough to receive the following information.

The Officers of the King’s Body Guard for Scotland, the Royal Company of Archers uniquely salute with their left hands as a result of a tradition that was born in Victorian Times: when presenting arms with a sword, the Officers also salute with their left hand as an additional mark of respect to their Sovereign. This tradition has developed into saluting with the left hand even when the sword is not drawn. The late Queen Elizabeth II very much approved and the King also supports it.