Sorry, but again I beg to differ, being a Scot myself.
Aye and Ay are pronounced the same - as in high or eye, and can mean yes, or still, always, on every occasion. You can confirm this in the Scots National Dictionary as well as by listening to Scottish singers performing this song.
Ae, as in Robert Burns’ poem Ae Fond Kiss, is pronounced ay as in stay, but means “one”.