I imagine Burns has been sung with every accent in the English-speaking world. Certainly when I was a kid in Canada singing Comin' Through the Rye, and as an adult in same singing Auld Lang Syne on New Year's Eve, it didn't and doesn't occur to me to lay on any kind of accent other than my own ...

Having said that - I don't know about the "yo-yo accent" - whatzzat?