"Ay Waukin, O" is credited to Robert Burns so it seems common sense to me to write the title as it was originally published rather than according to the various interpretors of the song. The online sources I see re Burns use the spelling Ay, and I have always seen it pronounced "aye"

Another well-known Burns song is written as "Ae Fond Kiss" (is Ae pronounced as simply a long A?)

Burns mixed various Scots dialects and standard English as suited the sound of his lines, and perhaps according to sources of his lines which were often adapted from folk sources. By the way, Ay Waukin, O may have been inspired by a Gaelic song "Cadal Cha Dèan Mi", I won't sleep, which is sung to a fairly similar air.