...you do to Sugarland's "Stuck Like Glue?"

I would swing =]

I prefer the swing when an East Coast, or triple-step, works. But that style of the swing is not best for a song of this tempo.
Still, you would have to do the swing to this song. I would lean toward something in which you may be able to incorporate some country two-step turns or variations, etc., to a basic swing.
I believe there is a style called Western Swing (not to be confused with West Coast Swing) that combines swing with Texas Two-Step and other country flavors. Don't see it much around here in the Midwest, though.
If I knew anything about the Shag, which I don't, it's possible that style, fairly common in the Carolinas, would work as well.