A few thoughts -
Mentioning to your son that he does not look relaxed may make him feel even less relaxed... unless you can partner that statement with something along the lines of, "can I show you what helps me?"
So here are a few tips... Did you ever have a manicure, in which you also received a hand massage? Very relaxing. There are tips online for giving a hand massage, and also for a person to massage their own hands. There are several youtube videos and also pictures paired with descriptions on wikihow. If you try hand massage for yourself and find it to be beneficial, then you can honestly offer to show your son something which has helped you.
Stress balls and fidget toys are great, but there can be a limit as to the time and place for these... just as there can be for a hand massage.
Is he athletic... or does he have energy that he needs to burn off... might a sport or physical activity help? Possibly it is not about his hands per se, but rather an amount of pent up energy that could be released by jogging, martial arts, swimming, basketball, a bicycle ride, etc?
One more idea is knitting.
...according to several reports, more men than ever are knitting in the U.S. and the U.K. (In the U.S., the Craft Yarn Council estimates 2 million boys and men now knit). These are college students, doctors, musicians, stockbrokers, Hollywood stars, inner-city youth, snowboarders — all who are taking up the 1,800-year-old craft not out of necessity but because they find it meditative, restorative, creative, or an avenue to connect with others.
It is possible that a combination of strategies may help him feel more relaxed and also project an image of being relaxed.
