P.G.
Hi J. - my son is on the spectrum is 7, and is integrated in public school. Are you comfortable giving examples of his busy hands? Is he flapping them? If yes, that's usually a sign of happiness :) Yes, it's different, but if you know what it means, its easier to not be embarrassed. My son flaps when he's REALLY happy, so it's not frequent but it's there.
This is called "stimming", and there can be a lot of reasons behind it - here's a site created by autistic adults that might help you out re. understanding what's going on.
http://what-is-stimming.org/so-what-is-stimming/
Also, ask your son about it - how it makes him feel or helps him. You may find that it is something that is GOOD for him and helps him de-stress. If it's big and disruptive (not embarrassing, but actually problematical), finding a "replacement stim" is better than trying to stop it, because if he can find something that works himself, chances are it'll be better for him than being MADE to stop and having something else crop up that creates more of an issue.
The best thing to do is realize that it may bother YOU more than it bothers him. If that's the case, you'll need to find peace with it.
Here's a great blog that you might enjoy and find helpful: adiaryofamom.wordpress.com
Feel free to ping me with a persona message if you want to. :)