The best way of achieving this is probably to use Parental Controls. That said, I'm not sure what kind of control you'll have over Safari (never used it here myself). Note though that even if you disable it, your son could still easily clear out the history and cache from the menu, erasing any browsing history. He could also use a different browser which would negate any settings you've setup for Safari.
The greater issue is what your son is doing. At the risk of sounding as if I'm telling you what to do, perhaps you should just address this with your son. If you keep trying to find ways to block it, he'll find ways around it and you're left with a constant ongoing battle that won't solve itself. I just gave two examples of how he can get around a disabled private browsing setting and there are likely many more. Talk to your son because otherwise, you won't resolve this anytime soon.