Greentext

Silverhand is explicitly a high functioning cyberpsycho in the tabletop RPG books. His "breaks" manifest as his hand talking to him. It's one of his notable character tics. In the books it's a big part of why he thought he could pull off the Arasaka bombing.

More info than anyone needs:

Mike Pondsmith, the creator of the setting, has said that cyberpsychosis shouldn't be treated like a pure numbers game set of RPG rules. It's intentionally modeled after real world drug addiciton. Some people will naturally have higher or lower tolerances, and having a strong support system around you like V's usually blunts the effects. It's countered by a stat called humanity, and Pondsmith has stated that a person's own beliefs about how human they are can impact it.

Cyberware was slightly rarer when Johnny was running around, he's an AWOL soldier with untreated PTSD, and he has a pretty shit "support system" mostly due to his own actions. Given the views he already spouts about corporations, people, and the world in general it's not hard to imagine that he's not stable without the arm. He doesn't have a high opinion of his own humanity. The arm then becomes a constant reminder of the humanity he's lost/given up.

Adam Smasher is explicitly a socio/psychopath already, before cyberware, so there's no humanity for him to lose.

V has Johnny in his brain to effectively act as a second "person" to help soak up the negative effects. Plus, videogame. Bend the rules to allow a better power fantasy.

I heard a pretty compelling case for it recently. In the cyberpunk books, Johnny kills several people and blames it on his arm. There were some other points, but I can't recall them right now.