Hi OP
You sound a lovely person who had a horrible experience the other day. I just wanted to give another perspective on the thread - but please before I add this don't think I am in any way doing this to make you feel bad because I'm not!
I had a similar experience the other day to what it sounds like the man your dog barked at had. I have grown up with dogs, used to work in a kennels etc but don't have a dog of my own at the moment as I have young DCs. I was in the park early the other morning with a friend as both our kids are going through the early morning waking phase! There was a man walking a large GSD who was muzzled. The dog somehow slipped his lead and made a beeline for us ( possibly because of the children mucking about). He circled us and was barking, lunging etc. My DC are confident around dogs, but luckily did as I said and stood still. My friend's DC is already frightened of dogs and starting screaming hysterically which of course led to the dog becoming more frantic. The dog then began to focus his attention on the child coming nearer. My friend was also hysterical by this point.
Another man walking his dog ran over and the dog then turned his attention to this man's poor dog. He dropped the lead and the dog chased the other one. Luckily before anyone was hurt, including the other man, the owner manged to regain control of the dog.
The owner was devastated and hugely apologetic - explained he walks early, muzzles and always has on a lead but the dog had somehow slipped it. He was in tears. Dog had never gone for anyone before. I suspect the dog probably couldn't have hurt any of us. Even with my confidence with dogs though I must admit it was a very scary experience and it was hard to stay still.
I genuinely had some sympathy for this man and could see he wasn't being irresponsible it was just one of those things. My friend and the other dog owner were less polite it must be said.
Unfortunately my eldest child is now terrified of any dog. His friend hasn't been able to leave the house and becomes hysterical if he sees any dog.
I'm only mentioning this because sometimes even for the best owners accidents happen and they can have consuquences which, if you are out walking in a public space, can affect others. I get the impression from your OP you have this concern and I guess I just wanted to say that is a genuine concern.
You sound a very caring, sensible person who obviously knows your dog well and who will make the right decision if you trust yourself - and by that I don't mean necessarily PTS, more just that you should have confidence in whatever decision you make.