AsianMom,
I think it is great that you are trying to help your son fit in with his peers, but by taking away an important coping mechanism, which he uses to reduce anxiety and focus, you are denying him his own way of dealing with stress. I am trying not to judge you, but as a 29 year old, married, mother, I think punishing him for coping the way his brain needs him to is harsh.
I stimmed as a child, by flapping my hands, but my family and friends chalked it up to just a funny thing I did. I would wring my hands when I became excited too. I didn't realize I was doing it until after I had already started and/or someone pointed it out. I eventually stopped doing this in front of other people (by 6th grade), b/c I realized that other people did not do this.
I still stim, but I when I am in public, I carry something soft in my pocket, like my baby's sock and I rub this when I am feeling overwhelmed and am starting to zone out. This usually helps me calm down, without anyone knowing what I am doing. Maybe your son likes soft things and they calm him down. Maybe he could carry a piece of soft cloth in his pocket and he can hold it in his hand when he feels stressed.
You are actually creating more stress for him by not letting him do what his brain is telling him he needs. You are also probably creating a lot of shame for him at the same time. He will resent you for your oppression later when has learned to control the stimming, on his own. Please let him do it in his own home, at the very least, so that your home is a place of acceptance and security for him, coupled by an explanation that stimming in public is okay if he really needs to do it, but that home is a better place.
Also, there are remedies, such as Lemon Balm, which help with anxiety, stress, and focus, and it is also an anti-viral herb without side effects. I wish my Mom would have known about it when I was in school. I found school extremely stressful and I am sure your son does the best he can.
I realize you are NT, so you are not sensitive like your son, but your son will be more apt to take social risks, such as making friends etc., if he knows, no matter what, he is accepted and appreciated at home, stimming and all.
Tallgirl.