1) To remove all weapons but not picks you could either remove all weapons form the raws besides picks and bo staffs, but moody smiths would still make bo staffs, or remove the weaponsmithing skill and make a reaction for the forge that uses the armorer or blacksmith skills to produce a pick with equal material.
2) Masks and belts can definitely be made and act as cheap armor. Goblins already have a mask item that they wear on occasion, but to make it a wrestling mask you may want to increase coverage to protect the entire head and facial features.
3) Use a reaction for the bo staffs, like picks, that accepts only a log of a new wood definition with the density of silver that is also made through a reaction that converts a log of any wood into it. This would make playing elves weird, if you wanted to do that, because players would have to manage stockpiles to make sure the wood conversion reaction isn't converting the silver-wood into silver-wood.
4) Humans can be kung-fu pros, but removing grasp would mean they couldn't punch, or pick up and put on clothes as an adventurer. I wouldn't suggest modifying their body at all, but instead make them naturally skilled strikers and kickers as MAIN attacks, and make sure their bite and scratch attacks are SECOND rather than remove their teeth and nails, so you could still knock their teeth out. Then they won't use teeth or fingernails in combat unless they can't punch or kick, so they'd never use their scratch attack because that would imply they have a functioning hand, which means they can punch. They'd only bite if someone pulled a Monty Python and ripped their arms and legs off or otherwise disabled them. You won't be able to prevent them from wrestling as long as they have limbs to use, and having them crawl around without arms or legs would be too weird, and prevent punching or kicking.
You can make their punches and kicks stronger by reducing their [ATTACK_CONTACT_PERC:
100] to
1. That means they'd put the same amount of force behind 1% the surface area, for a very powerful attack. You COULD also increase the thickness of their muscle tissue on their hands and feet, but reducing the surface area of the attack should make it fairly impressive anyway.
On the note of natural skills, I'd suggest giving each race roughly equal natural skill in the fields they will use in combat.
And make kobolds tiny, raging berserker animals that use their teeth and claws, but let them punch and kick as well. Reduce the surface area of their bite and scratch attacks and make them all MAIN and they'll be about as effective with those as a human is with punching. Give them the PRONE_TO_RAGE tag with maybe a setting of 10 and watch them go bonkers on anything in site, then run away if and when their rage subsides. Would make thieves like little assassins.