There used to be a chapter of the World Peace Council in Berkeley, but this was decades ago. Back when, it had several people who did draft counseling and had the drill down pat. It might still be around. They were low key and had been doing the same thing for conscientious objectors since the early fifties.
And of course try Michael McIntyre's suggestion, CCCO, and asked them who they recommend locally in the Berkeley-Oakland area.
In the meantime, I would register just to keep from breaking the law in advance. Your son might have been automatically registered by his high school---and if not there, then colleges do it on an eighteenth birth date (I think). BHS gave my kid a form he had to fill out before he could graduate, even though he was seventeen.
Some time later, at some point, you can argue that registering for the draft was simply following the law and had nothing to do with your intentions to refuse induction. If you want to get technical, I think your son could write a letter stating his objections and reasons, date it, and have it notarized and put it in a home file. If they ever re-instate the draft, then he can re-start this file, update it, write some other things and mail it to the local draft board, if they ever open those things again. The point to writing something now and getting it officially dated is to establish a record with a specific point in time, prior to any need to do so.
I really wouldn't worry much about it. No matter what the bullshit media claims, I think serious support for WWIII against the Islamic hordes is about as thin Bush's vote margin in Florida.
Chuck Grimes