This is definately something where each of us has to find their own way. I am no expert, having only dispatched 20 birds last summer. I wasn't crazy about either the knife or the hatchet. But there is something to the technique. My first bird I tried with the knife, found it bloody awful, and gaspy. But I later discovered I'd done it all wrong, cutthing across the throat (severing the windpipe) instead of just on each side below the jaw. That seemed less gorey. At some point I switched to the chopping block, but I had trouble getting the birds bled out as well as they did by slitting the throat. So I stayed with the knife method.
But I was going to suggest you may try using a machete instead of a hatchet. Hard to miss if you use a nice chopping block and the two nails to help stretch out their neck. There's really no pleasant way to accomplish this. But what about wringing their neck? That is pretty easy and quick, just a little tougher to get them bled out.
I have reservations about shooting a chicken. And I'm not opposed to this as a humane way to dispatch an animal, I put down my last dog in this manner and have absolutely no regrets. (one moment sniffing flowers, the next it was done) My concern is the birds are a small target, and as mentioned previously, after the first they will be spooked and scattered. In the excitement I'm afraid you may lose track of the bullet trajectory. You need to make sure all is clear for a great distance, preferably shoot sharply down. .22lr travels far and fast. There are no 'accidents' when it comes to guns, just mistakes. No offense, but if you are coming here for advice about using a gun, I suggest you don't.
Good luck to you.
