Oh dear. Not a subject for Christmas Day, is it?
I used to line a bucket with a plastic bag, then hold the quail over the bucket in my left hand with fingers two each side, over his wings and either side of his neck, facing towards his head. Then I positioned a pair of secateurs on his neck, holding the sides, and with contact at the back of the neck, just behind his skull. Then you pull firmly downwards whilst twisting the neck sideways. The aim is to dislocate the neck at the joint just behind the skull, rather than to cut off the head, although this may happen. I found the secateurs made it possible to grip the tiny neck precisely and firmly in the right place and hold on firmly when you push down and twist. There may be some blood, (hence holding him over a bucket) and it’s possible the head may come off, but the main thing is to do it quickly and be decisive, so he dies as fast and painlessly as possible. As with a chicken, the quail may flap his wings for a while after his neck is broken or after his head comes off, but this is just a nerve reflex that shows he has actually died. The head will flop to one side if it’s broken at the neck.
I did this the first time to a quail hen who had been so badly injured by a male that he had torn away an eye and most of her face, bleeding badly, so there was no hope of recovery and I felt it was best to put her out of her pain. Of course you could take him to the vet for a whiff of gas if you can’t face the job of putting him down, but I’ve always felt that as a keeper, I needed to know how to cull a bird, chicken or quail, in an emergency, and then once I had done it a few times it seemed good usually to do it quietly and efficiently myself. I couldn’t have left that injured girl to wait for a vet’s appointment. But it is a horrible job, whether it’s a hen or a quail I always feel bad afterwards even if I know I’ve done a proper job, and if you feel you would rather take him to the vet to be pts, that is a perfectly sensible choice to make. You can’t even keep the males together in a separate run as they do it to each other!
I hatched two consecutive batches of chicks before I found out that the adult males were such a problem. Out of the 17 chicks hatched in total, there were ten males and seven females. I had to cull one injured female and then all the boys. After that, the six remaining girls lived happily and peacefully together for some years and laid hundreds of lovely little eggs. But by that time I had decided not to hatch any more, because the boys caused such grief, to the girls as well as to me!