There seems to be no evidence at all of an earlier song which involved transformation. The earliest known (and incomplete) text was published by Robert Jamieson in Popular Ballads and Songs (Edinburgh, 1806, I 193-195); it was provided by a Professor Scott of King's College, Aberdeen, who got it from one of his maidservants. Jamieson had recalled the story (but had "forgot the terms in which it was conveyed") from his own childhood.

It's the only variant ever recorded in oral tradition in Scotland, seemingly. As in later forms, the shooting is merely a hunter's mistake made in the failing light of evening. The supernatural element consists solely in the dead girl reappearing as a ghost.

The song was quite common in Ireland and Southern England, having been published by various broadside printers. A number can be seen, under various titles, at  Bodleian Library Broadside Ballads:

Molly Bawn / Whan etc

Wherever the text published by Jamieson came from originally, the broadside form seems to have started out in Ireland, and English variants are frequently sung to Irish tunes. Commentators have frequently waxed lyrical on the subject of swan maidens and magical transformation, but there's no compelling reason to think that is anything more than romantic wishful thinking. Hunters shoot people all the time under the impression that they are game.

I doubt if any version of the song mentions poaching; Jimmy is described as "a hunter" or "a fowler". In England, swans do not belong to landowners; technically they mostly belong to the Crown, so far as I remember. I have no idea what the legal status of swans was in Ireland in the late 18th or early 19th centuries, but the song certainly seems to take for granted that there was nothing remarkable about shooting them.