Wolverine's hands are rated "E" for everybody who's stupid enough to get in his way. However, his upcoming PS5-exclusive solo game might be for mature audiences only.

In my doc for Game Mess Morning starting right now, I've written that we're going to talk about The Coalition's next game, Wolverine, and the chances of a Titanfall (and lots more TF Legends details). https://t.co/3HFFcqEL2j
— Grubb (@JeffGrubb) February 2, 2023
According to Giant Bomb's Jeff Grubb, Insomniac is targeting a "Hard R" rating for Marvel's Wolverine, or "M for Mature". Grubb mentioned that Marvel's Wolverine will likely involve dismemberment as a default, since that's kind of what happens whenever Wolverine pushes his adamantium claws in and out of his knuckles.
However, Grubb clarifies no one is forcing Insomniac to do this, giving examples of how other games workaround to avoid such a rating. Finally, Grubb reveals that Insomniac's game will take place before Wolverine joined the X-Men. We can only presume then that it might take a page out of X-Men Origins: Wolverine's book.
It's hard to imagine Insomniac being creatively driven to a corner just because their upcoming game will feature the very brutal Wolverine. You could argue that the Marvel's Spider-Man series are just a few key changes away from being rated M.
Ultimately, Marvel's Wolverine could have an M rating due to a combination of violence, gore, and mature subject matter. Keep in mind that Wolverine wasn't exactly traveling around the world and soul-searching before he came across Professor Xavier and Xavier's School for Gifted Youngsters. Not to mention, being that he's very old (several centuries old), Wolverine carries a couple of generations worth of trauma on top of being experimented on for the Weapon X program.
With that said, since Marvel's Wolverine is targeting a late 2024 or early 2025 release, things can and will still change from now and then, especially if it gets pushed back to a later date.
For now, PS5 owners can look forward to the launch of Marvel's Spider-Man 2. Insomniac and the game's voice actors are insistent that it's still set to launch later this year.