I don't feel shame for killing a fox that has killed my birds. My birds are contained and if a fox breaches it I'll trap it and kill it. I had a fox kill my favorite bird several months ago during the day. I caught the fox and permanently relocated it. It's not against the law here to kill predators if they are killing our livestock.A .22 to the head isn't going to cause much, if any blood, at all.
In years past I used leg traps but since people have been dividing their property into smaller parcels and selling some of the parcels, we have had quite a building boom in our area. Now I've been using live traps. To catch the fox that killed my Gladys, I set them out and let the fox take the bait for a few days then set the trap and bingo, I caught the fox. It was mangy and stank.