The place to look for Scottish emmigrant songs is not Scotland, but the lands recieving the emmigration. For the Highlands people left in droves for USA (the Carolinas) Canada ( Cape Breton & mainland Nova Scotia, PEI, eastern NB, Southeastern Quebec, Bruce and Glengarry areas of Ontario, and Manitoba), Australia, and New Zealand.
At the time of emmigration 1770-1850 most were Gaelic speakers and their laments for the Old Country were sung in their mother tongue. A song of a Highland emmigrant would never have been in Lowland Scots as that was never their language. Of these areas only Cape Breton Island still has descendants of these pioneers who still speak "the Gaelic" and some of these old songs still exist.