Luckily for me I do not have any problems with barking dogs, and I am so sorry for all those that do. Cats is also my major problem, but there are plenty of threads about cat problems so I will not start.
However, I will add my humble opinion: Diddy, you must get this problem sorted out. Your neighbour is making your life a misery. By all means try the sonic thing but if that doesn't work, what will you do? You have to complain to the council and to the RSPCA if you are worried about the dogs' welfare. I seriously doubt you will end up being shot, but if you are worried about it, lock the doors for a few days and be ready to phone the police at the drop of a hat.
I know it's annoying when you have to sort out problems that you have not created and force others to take responsibility for their own actions, but if you don't this problem will just get worse. If you ever wanted to sell your house, you would have no chance if dogs are constantly barking.
Just in case anyone is wondering, I love dogs. I would love to have one, but my job means it would be alone for most of the time and I would not be able to walk it properly on work days. So I don't have one. I personally wouldn't allow most people to own dogs as they are not able to look after them properly, then we would solve the problem of most of the dog mess in public places, people being bitten by dogs that are not trained properly, and noisy dogs making neighbour's life a misery. When I retire I may get one, but not before.
I wish you luck.