This would encourage players to sell their mediocre weapons.
I'd rather see
One of the categories contains at least one weapon that you own
running with an empty equipment slot counts as fulfilling the restriction
You have to equip at least one weapon (can't play with no weapons), therefore there should always be a weapon you can equip at all times without restricting you from getting the full reward.
If you don't own any of the weapons of a category and you don't consider one of the weapons worth getting, the weapons probably would be of no help in the game mode anyways, no matter how you mod them. What's the point of telling a player they have to equip a weapon that they will never switch to, that they'll just carry around for show? Just make it so players can run an empty equipment slot instead.