I was thinking, what if there were arm wrestling tables in a few places? The Sly came to mind as a likely spot for one, and maybe Grunen's for topside (or maybe topsiders miss out).
Mechanically, it would work by checking the participants strength and endurance, maybe in a few 'stages', with repeated good rolls required for victory. It might be a non-violent way to settle who's bigger and tougher–or an invitation to the kind of shit-talking that starts a blood feud.