This is what I'd do. Count the material against his weight, immunity to broken bones (if you're not running wounds, then well...pick something else) and give him simple claw damage.
Keep in mind that for the most part Wolverine only had Adamantium plated bones. He didn't have a solid Adamantium skeleton. (the lore is obviously inconsistent here). And since we're assuming this was done magically, just *wiggle fingers* magic away the need for a healing factor to overcome all of that nasty metal all over your bones. Unless we're saying he has a living adamantine skeleton. Then that's just...weird.
But the skeleton itsself would provide no other protection to the dwarf's meat, 'cause ya know, the meat is on top of the bones.
Maybe some kind of psionic/psychic protection if you're not running broken bones in your game. I don't think wolverine ever had any sort of mental protection, but again, this is only if you're not running broken bones.