Sorry but I think that's a terrible terrible way to restrain your dog.
I am sure you want the best for your dog which is why you need him to stay put and not risk your neighbour who has every right to shoot your dog but this option would be cruel. It may not even work!
Your puppy is being rewarded when he leaves your garden with the excitement of chasing and killing chickens, I suspect that any shock the collar would give him he would pail into insignificance against the thrill of the chase. So he would be being harmed with no effect. There are cases of these collars burning then fusing to the necks of dogs who have a high case instinct.
In any case, your border terrier is only doing what his breed is telling him to do.
Your pain free options for restraining him (without fencing) really come down tying him to a long line while he is outside (with a harness not collar, he will prob be able to slip a collar). And training, lots and lots (years and years) of training. Even then he will always have the chase / kill instinct now he has discovered it.
If that is not practical for you then he is not the dog for you.
Personally I am surprised that they even allow these fences to be sold in this country. Like prong collars I think they should be banned.
Good luck