Why not add boxing to the game? Or martial arts of some sort. I mean, it is possible to enter the clockworks completely unarmed.
I have two ideas for this potential method of damage.
1. Certain armor, helmets, shields, or sprites can provide perks or bonuses for unarmed damage.
2. A new equipment is added to the game: Gloves. Different gloves do different damage, just like normal weapons. They can also have different attack patterns and charge attacks. Like boxing gloves deal out slow, powerful attacks, and has a charge attack that is one massive blow. Ninja gloves deal fast blows, and have a quick, multi strike charge attack.
I know this entire concept is HIGHLY unlikely to actually make it into the game, but I think it's a cool idea and I'd throw it out there.
Personally I like the idea of new gameplay opportunities, but your idea here isn't too far off from what we have already in the game.
Physical punches or strikes could probably be classified under "sword" actions based on swinging the model's arms back and forth, and the tortofists already have an action that looks like a "punch" and those are guns.
We have the "Power Mitt" which is a shield that fits of the wrist of knights, so it's likely that gloves, cuffs, or shackles could fit in as weapons of the sword variety.