Mick: You plans for the electric fence, etc. sound good.
What follows below are for those who can have guns and want to use em.......although I think the fox will win that battle most of the time. They will come around when you are not........
This is the image used as my avatar, and that pretty much is me, including the double barrel shotgun. It once belonged to my grandfather. 12 gauge, 28" barrels with modified and full choke. When used with #4 buckshot, one shot is the rough equivalent to 22 to 24 .22 rifle shots spreading out to a 3 to 4 foot circle at 40 yards, which allows for a wide margin of error on a fast moving target.
Anything up to a large dog inside 50 yards is in serious trouble. They hit the ground graveyard dead. At close range, you could turn something as small as a rat into hamburger.
With the correct loads, even a diminutive single shot .410 inside 20 yards is a lethal weapon for anything short of a bear.
Shotguns offer potent short range firepower with far less worry about what exists downrange of your target. Shooting a rifle in a populated area is no trivial thing.
Years ago, a local guy found himself in the news after he shot at and missed a rabbit in his garden. He was shooting up a hill. His missed shot traveled over half a mile.....including over an Interstate highway, and when it came down, hit a women in the head and killed her dead where she was standing. He was convicted for manslaughter and served time for it. Just saying.