I just don't like how crutches are the only option to handle amputations. Even if you ignore the arm issue, there other ways to deal with leg loss. I've heard of double leg amputees using what are basically skateboards to get around, how about that? I think a dwarf can manage to nail some wheels to the underside of a wooden board.
As for hands, I don't like hooks either. A hook is a poor manipulator and a poor weapon, and I like to think even dwarves aren't stupid enough to attach a sharp metal hook to a creature prone to random fits of domestic violence. I could be wrong on that, though.
It's been brought up already, but Götz of the Iron Hand's prosthetic seems completely doable with DF's tech level. From the pictures I've seen, it was just a poseable hand, no fancy mechanisms or anything special. Just metal for the hand and leather for the straps, nothing a dwarf doesn't deal with regularly. Articulate enough to hold a weapon or tool, but not enough to match a real hand in their use.
Replacing a limb wouldn't be a perfect fix no matter how well made the replacement is, even today's prosthetics can't beat the real thing. Wrestlers would have difficulty maintaining a grip with a hand that had no muscles, craftsmen would lack the dexterity for finer works, and movement in general would be awkward with any kind or replacement leg. But it is still better than nothing.
There are slight, SLIGHT benefits to an artificial limb. A prosthetic isn't connected to the bloodstream or nervous system, meaning no bleeding and no pain if it gets severed. It would still be destroyed by a severing strike, though, and you'd need to build another. No, an artificial limb should not increase chance to block, but an adamantine arm should be able to deflect the strike of a copper sword.
Also, a dwarf with two replacement legs should be able to walk right through a puddle of syndrome-inducing substance without consequence for the same reason.
However, the disadvantages should outweigh any benefits, while still remaining better than crutches or nothing at all.