What obligates something for immersion is that it is a utensil for eating with or preparing food with "כלי סעודה" Anything else has no obligation. See Shulchan Yoreh Deah 120:1, Aruch HaShulchan 120:30.

Example. A mohel needs to peel a orange and the only knife he has to use is his mila knife. So while yes it's a metal utensil, and yes it can be used for peeling the orange, since it's not meant for food prep or eating the knife does not need to be immersed before using it to peel the orange.

In our case since the primary purpose of the prosthetic hand is not for eating - even though that is certainly one of the things that he can do with it - it would not need tevilah. Again the key being "כלי סעודה" vs. anything made from metal used for eating.