surgery is too cruel.. how about putting him up at a friend or relative's place for the time being? or send him to some boarding house while giving him training?
It's really quite simple, and has worked for two dogs of mine (consecutively).
Every time they bark, yell at them and smack them.
If you start this while they are young, they will never even start having a barking problem.
I have no words to describe such cruelty.
Where I live there are also many dogs that barks every night, nevertheless I never told my neighbors to take them to the surgeon to... I can't even think about it... poor beasts!
I suggest you to avoid your pet this humiliation.
IMHO your neighbors should go to the surgeon, not your dog.
You said your dog is a border collie... that's a working breed... very smart dogs that are lovely to have around as long as you keep them busy. Many working breeds (including border collies) will exhibit problem behaviours if they're bored and/or lonely.
I suspect if you were to surgically "de-bark" your dog, he'd start showing other problem behaviours (really, barking isn't so bad.)
Give your dog something to do. Kong makes a good toy you can stuff with treats and stick in the freezer, keeps a dog busy for a while. Tie a knot in a tea towel, get it wet, stick it in the freezer... play with the dog with it, encourage him to play/chew. Leave the radio on when you leave the house... etc, etc.
Get creative about finding ways to keep your dog busy. And train him. Lots of positive reinforcement for good quiet behaviour, and a nice, firm "No" (and no attention) when barking.
There's lots of good resources online if you need help.
I would recommend avoiding "punitive" or "physical" methods with a working breed. Ususally backfires... works with some dogs, and breeds... but not always a good idea, especially not if you already have aproblem.
As the dog is a border collie, he is or should be a working dog. They were bred to work and are not suited to unit living, or even on a house block for that matter. That is the core of your problem. He is bored and needs to get out in the countryside and run around. It is most likely that he barks to release pent up energy. I think you have a choice of having him debarked or finding him a home in the country, as hard as it may be for you to part with him.
I lived on acreage for many years and had cattle dogs there, which have now gone to live on a friends property as I am now living close to neighbours. I have been researching smaller dogs of a calm disposition who will enjoy lying around the house and just having twice daily walks. I having decided that a cavalier spaniel cross would make a suitable pet, but haven't got one as yet. I am looking forward to it though.