Snares are legal. They work 24 hours a day. You find where the foxes are running, set the snare, and leave it to do its work. I've killed several foxes on the same runs over a few weeks. A dead vixen, hung on a fence, will often attract others to their death.
The unfortunate thing about foxes is...the more you kill, the more you have to kill. They are territorial, so every time the territory becomes vacant another moves in. So there is an argument for trying to live with the foxes you have.
Killing vixens in February/March time can help toward a fox-free summer as it's unlikely that another pregnant vixen will move in so late in the season. The bereaved dog fox, without cubs to feed, will not be such a danger to poultry...for a wee while at least.
The worst case scenario is that you kill the dog fox and leave a vixen to rear cubs on her own. In that case she will definitely be looking for easy meals, and will often kill in broad daylight as the cubs grow and increase their demands on her.
I have killed many hundreds of foxes over the years using snares, gun and rifle, lurchers, terriers to bolt them to the gun or nets, and even gas, but they still come, and the minute my guard is down they are at my stock again. It's a constant commitment...that's why I work snares.