I absolutely understand where you're coming from OP because I would be horrified and devastated too, and would feel so awful for the child who was hit.
That being said, I don't think approaching this from the perspective of shaming your son is going to help. Worrying about prison and him not having a conscience is wide of the mark; LOTS of children struggle with control and emotional regulation, and lash out as a result. Of course that doesn't make it ok, but it does mean it's a solvable problem.
You can't teach a child emotional regulation by telling him he'll end up in prison one day. When he loses his temper and hits someone, he isn't thinking about long term consequences. He is acting irrationally from a place where he is out of control. Your job is to help him with techniques to build emotional regulation so that when he's feeling stress or pressure, he can make alternative choices which don't involve hitting.
This is why something like martial arts training might help him - of course you fear it will just make him better at hitting, but actually a lot of the training kids receive in these sports is about controlling your feelings, planning your actions, and maintaining self control. These could be very helpful for him.
I think you should approach him from a place of empathy. Not one which tells him it's not his fault - you're right to firmly uphold the position that hitting is unacceptable, and his punishment by the school is fair. But don't make him feel he's a monster to you. Tell him you understand that in the moment he loses control, that lots of kids struggle with this too. He's not alone in this challenge, and it's not insurmountable. Tell him you're going to help him learn methods for better emotional regulation, so that in future when he feels that way he can make better choices.
And then do your research - find what works for him. The key to emotional regulation is you have to practice it when they're calm and ready to learn, so that it becomes almost habitual. Try researching breathing exercises, yoga, the squeeze-release reset, the anger thermometer, etc. Try reading The Explosive Child, it's an excellent book.
This problem won't be solved by anger or shame, but it is solvable.