Wayne Rossi's post yesterday mentioned something I hadn't noticed: the equipment list places melee weapons in order by the length of the weapon, which is thus also related to the weapon classes in Chainmail. Bows are in a separate group after melee weapons, in order of increasing range, and crossbows are also treated as a distinct group.
That simplifies determining who strikes first. Just use the order of weapons. Anything not on the list uses an equivalent weapon that is listed. Scimitar or cutlass? Basically swords. Small hammer? Basically maces. Warhammer? Mor like a battle axe, although it can't cut through things, as a battle axe could.