Couldn't see anything in the song that puts a date or period to it. Although definitely written in the dialect of the N-E of Scotland, there is no reason to automatically qualify that the regiment she refers to has to be Scottish (Example: "There once was a troop of Irish Dragoons cam marchin' doon through Fyvie-O" - N-E Scotland identified as the area, non-scottish cavalry regiment).

If the song pre-dates French Revolutionary/Napoleonic times by about fifty years, an alternative Scottish cavalry regiment to the Scots Greys did exist - 17th Light Dragoons (raised 1759 - disbanded 1763).

In an earlier link on this thread there is a site that lists songs of the Napoleonic era. One of the songs mentioned was "The Female Drummer" - no doubt it was sung by soldiers during the Napoleonic Wars - one version actually mentions "the seige of Valenciennes" (1795), but the song is older than that! Earliest I have been able to trace is around very early 1700's and the reign of Queen Anne

"When I was a young girl, age of sixteen
I from me parents ran away and went to serve the Queen"

The same might be true of "The Lichtbob's Lass".