I absolutely agree with the not jumping into the castration route. It is a myth that castration "cures" male dog aggression IMO! I have a castrated male dog, Ben, who is extremely aggressive towards some male dogs - we have figured out that it is large dark-coloured/black male dogs of spaniel-sized upwards, particularly those breeds with floppy ears such as labs, pointers, Weimeraners etc. etc. etc. Erect-eared dogs like GSD's (with a few exceptions esp next door's!), collies, mals, huskies, akitas, he is pretty OK with. He is a low % wolf cross, so we have the theory that he cannot "read" dogs with floppy ears.

All females of any colour or size are absolutely fine. All small dogs of any colour or size or sex are fine.

My personal opinion is that there is nothing "wrong" per se with this - nothing that can be fixed, it is just the nature of the dog and we have to live with it. With the OP's boy, it might just be as it is with Ben - his nature.

Bitch on bitch aggression and dog on dog aggression is common - after all they are animals. Back when we were living in caves, most likely we were similar!

Some dogs can become same sex aggressive when they reach maturity.

We had experience of dog-to-dog aggression when we first got Duke (GSD crossbreed) and he was aggressive to all dogs irrespective of sex and age. We did have him neutered because we would not breed from him and I personally won't keep an entire pet for long-term health reasons. However, I think this hormonal change made Duke more "attractive" to some dogs who wanted to mate him which did not help our cause. Also Duke had already learnt to be aggressive so changing hormones did not change his learned behaviour. I can appreciate your concern regarding anaethestic but it may be worth talking to your vet about that and your dog's behaviour.

You mention your dog is aggressive to those that approach you or your home so how do you know they are all male? Is your dog aggressive to your son's dog if you are on neutral territory and you are not paying attention to your son's dog? Might be worth doing some sleuthing, so long as you do so safely, to work out the specific triggers whilst bearing in mind not to set this behaviour as a habit.

As Duke was new to us I worked on his obedience to commands and then walked him on and then off-lead with my friend's placid dog in a field with no other dogs. We built it up gradually from great distance to side-by-side. It was difficult re-training Duke living in a town as more or less every time we stepped out the door we met a dog so I took to being out at odd times with him. I muzzled Duke. Once I was sure I could have him off lead as he would recall to me I did so with him muzzled and he was much better as he coped by distancing himself from other dogs but couldn't cope when they ran up to us on-lead.

We got enough control that we were able to take Duke to a Battersea Dogs reunion event which was mobbed with dogs and he behaved beautifully but I could tell that it stressed him so we didn't do it again. I had wanted to do working dogs trials with him but it wasn't fair to take him to doggy events when he felt stressed around other dogs. We were also able to get a second dog who he loved and let Cindy boss him about. Once he listened to us he was good and he would allow one male dog we walked with to jump up at his shoulder with no reaction which amazed me.

Sounds territorial to me.
I would go for the castration route and I'd work on desensitisation methods.
Just my humble opinion of course, you must do what suits you and the dog.

Very nice story, Duke was fortunate to find you. (sorry to go off topic)