There is no real need for a big shot count if you're hunting. If I ever started hunting again I would be looking at a multi-shot Ultra or an S200 and get a multi shot adapter for it.
If you need more shots (I'm presuming you're travelling to your permission by car) I would suggest taking a bottle with you and returning to your car for a top up but an Ultra will drop 30 rabbits from 1 fill which will weigh a lot more than a heavy gun.
Good luck with your search.