As of right now, I can only find a map of nerve fibers, but not necessarily the individual neuron axons.
For example, here's a map of the nerves in the arm and hand. http://www.innerbody.com/anatomy/nervous/arm-hand
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No it is not possible to map axons at that fine of a scale between individuals.
You mention a possible use for controlling bionic arms. There are a bunch of problems with that approach.
If for some reason the issues I raised don't apply, there is another alternative: mapping. You don't need to know which axons you want information from, you only need to be able to record their activity (which you will need anyways to operate the prosthetic). Record the activity while the patient tries to move their finger, for example: now you know the signal you should transduce into a finger movement. The technical challenge, then, is being able to isolate that signal from all the other signals from all the other axons in the same nerve. This challenge is related to, though not precisely the same as, the challenge of isolating a signal in the EEG.