By the way, the idea of Unarmed as an auxiliary combat skill that can be used at any time is pretty cool and would work in almost any setting. People can be disarmed, guns can run out of bullets, spell slots and mana can run out, quivers can get dry, swords can break, but you can always do an unarmed attack at any time.
It can also be a supplement, with stuff like grapples or opportunistic unarmed attacks in melee fights, etc.
Hell, you could have something similar with melee too - bayonets, gun butt attacks, bashing someone with a bow, etc.
One possible advantage: Unarmed is a less lethal than melee. It could be the "non-lethal/less-lethal" skill for Pacifists, or simply capturing people.
Maybe, but I could see this getting frustrating when players want to capture some important NPC, so they start their attacks with weapons and try to time it perfectly when to swap to unarmed to avoid a kill. Sounds like lots of savescumming
Introduce bleed/internal damage and fatigue mechanic, so you can't just toss a punch at the end and take a guy non-lethally after you spent the last ten minutes hacking him to pieces.
Open X-COM Mods actually do it pretty well, you can't just use a stunning unarmed/melee attack and take someone down 100% of the time, depending on the weapon/attack and health of the opponent, going non-lethal often has a chance of killing people anyway, "overstun" is a thing, bleed damage is also an issue, etc. This is especially an issue if you have characters using the more powerful stun alternatives (like baseball bats).