I know it's been pointed out, but I feel compelled to underline the point again:
BBs suck. They're not even decent against unarmored, relatively weak animals. In the ammo menu, disable BBs for hunters and give them small caliber or even medium if your swimming in the stuff. Removing the hunting labor from the pony you want to hunt will have them drop the BB gun, then re-enabling will cause them to grab up an appropriate weapon.
Really?
Does this work?
Because this changes everything for hunting in non-ghoulish biomes.
Disabling BBs in the ammo menu and replacing it with small or medium caliber will cause your hunters to drop the BBs in their quiver (eventually) and seek out said ammo.
They will not be able to use it, as they still insist on making use of the weapon they're holding (i.e. BB guns).
Disable hunting from said hunter in their labor preferences. They will drop their quiver of ammo and the BB gun. Remember to forbid any BB guns to prevent their use.
Re-Enable Hunting after they've dumped the useless stuff. If you have set them to make use of the other ammo in the ammo menu, they will grab a quiver, attempt to fill it with small/medium/whatever and then seek out an appropriate weapon that makes use of said ammo.
You will then have a hunter hunting with a bit more power behind them. As was pointed out, though, the wildlife is still deadly but I've had a hunter I nurtured up to Great skill manage to regularly hunt down large radscorpions with a steel combat rifle and medium caliber ammo.
Too bad I had to abandon the fort. My arch-nemesis showed up (Random Forgotten beast made of insane material and using deadly dust) and wiped my Stable..again...