New prosthetics are controlled by brain waves which seem to make the prosthetic an extension of the body in an "organic" way, in that we control all of our own limbs through the same brain waves and impulses. [scientists -- sorry, my understanding is rudimentary -- if I am misrepresenting anything, please let me know]
This bit of Purim Torah (with actual sources) seems to point to the idea that telekinesis (movement of an object using the brain) would be allowed on Shabbat, but the question is about moving something external to the body and one opinion questions if using brain waves is k'lachar Yad. Moving a body part is not exactly the same, as brain impulses are the normal way of moving body parts.
This question asks about prothetic limbs in halacha but doesn't address this aspect of controlling their electronics when the electronics are integrated into the body (I learned that attached body parts are not muktza but I don't know when a limb is or is not "attached" enough to become a halachic body part, unlike a car).
So would the electronic body part be able to be controlled on Shabbat by the brain of the "wearer"?