The tune is actually a pipe tune called The Green Hills of Tyrone and it is written in 3/4 time signature, with words added about 100 years later by Andy Stewart, and the name changed. Although it's 3/4, waltz styles don't sound right because it doesn't have the typical lilt of a waltz. I Cant think of a style that would work properly for this song. But I will take a look. I would typically not play a song like this with a style, just piano. In fact truthfully I wouldn't play this song at all unless my arm was being twisted. Heard it being murdered too many times when I played piano in pubs!
Take my advice and play Ae Fond Kiss and My Luv is Like Red Red Rose instead. Beautiful songs written by Robert Burns, perfect for the occasion, which both work well with simple waltz styles. If you must stray away from Burns, there is a myriad of well known lovely Scottish waltzes which are a joy to play as a medley using one of the waltz styles - I use the country waltz, and just keep it simple - the two I gave you above, plus Over the Sea to Skye, The Northern Lights of old Aberdeen, Road and the Miles to Dundee, Down in the Glen,..........to name a few.
Mike