At the tae kwon do dojo we attended with our son, there were very specific statements the masters would make the kids memorize about being honorable, never using their fighting skills to hurt or tease others, etc. If you are listening in on the classes, try to pick up on what statements are being made about when/where to use the martial arts skills being learned.
If you don't notice an emphasis on this, you should ask the master what their policy is and how often they usually like to speak about this during lessons; our masters would bring this up nearly every single lesson. (presumably because it is so easy for a kid with just a bit of training to whack another kid in a martial artsy kind of way and the whole martial arts training thing gets blamed, when in fact it's just kids being kids...)
We've found that bringing this up with our ds, using a lot of the same phrasing as in class, would help him realize more quickly when he was overstepping a line, same with the rules for scouts. The other day he was teasing his sister before a meeting and I just whispered something about scouts being kind, and he completely got in line, which was very good to see. (Granted he's 11 now).
And I do think there is something to your idea about his using this new skill as a way to connect with other kids, in absence of any other common ground -- maybe there is a way he could still do that without engaging in battle? (give a short lesson to someone? not sure, just typing out loud).
