you'll need to go to Game_Battler 3
Find:
# Calculate basic damage
atk = [attacker.atk - self.pdef / 2, 0].max
self.damage = atk * (20 + attacker.str) / 20
and edit it. The "attacker.atk" is calling the character's Attack Power, which by default, is only above 0 if they have a weapon equipped. You could try changing attacker.atk to attacker.str which would look like this:
# Calculate basic damage
atk = [attacker.str - self.pdef / 2, 0].max
self.damage = atk * (20 + attacker.str) / 20
This makes the Attacker's Strength and the Defender's Physical Defense the only two factors in Attack Damage, as opposed to Attacker's Attack Power, and Defender's Physical Defense, with the Attacker's Strength playing as only a multiplier. Doing this, makes it so long as the character has a positive number for Strength, they can potentially do damage (so long as the Defender's Physical Defense isn't so high to stop this). I'm not sure what kind of effect this has on the overall damage output, since I don't use the default battle algorithms anyway.
An alternate method would be to institute a script that defines each character's Attack Power without the use of weapons, but I can't help you there, but I hope the above helps.