Not Really
While, strictly speaking, it is true that the nervous system is a kind of electrical system (chemo-electric, in that nerve cells communicate using chemicals in the synapses), it's not a system that is easily hacked in the way you want to hack it.
For example, if I'm a mad scientist on a shoestring budget, I might want to tap into your house's electric system to power my grievously underfunded mad science lab. I can do this easily, because of Standards. Power is supplied in convenient amounts and code compliant electric wiring is fairly standardised. All I have to do is tap your house's supply line and siphon off some of your juice. If I do this before the electricity reaches your meter, you'll never even notice.
Or say I want to reprogram how an electric device works. I can easily review the device's schematic diagramme and insert my own parasitic device which can then integrate into the functionality of the device. E.g., a cell phone or tablet computer. Because all iterations of the same model device are constructed precisely the same way, I can insert my parasitic device on any one of them.
The human body doesn't work this way.
While it's design is sublime, it's actual formation is entirely bespoke. What this means is that, yes, there are regions of the brain that handle say the movements of the hand. There are afferent and efferent nerves that either receive input (from touch or heat or pressure receptors) and offices in the brain that receive, correlate, collate, process, and act upon those inputs; and there are other offices within the brain that determine & command actions to be done on a conscious level, still more offices that interpret the high level dicta and translate them into the various unconscious impulses required to carry out the orders and then nerves that carry the signals to the muscles.
Completely apart from the question of how this is actually accomplished and whether or not it's hackable; we need to consider the embryological physiology -- how it all got put together.
While there is a general (genetic) plan for the end product of the body and also a general scheme for how cells will express that plan (how stem cells can transform into nerve cells or muscle cells, etc): there are no actual schematic diagrammes for human wiring. It's not like you press fit a circuit breaker into the box, run the wiring & insert plugs and switches and junction boxes according to a blueprint, and then flip the switch expecting it to work. Embryologically, each muscle, each tendon, each nervous pathway "grows" organically, sort of pushed out from the original fertilised egg and evolving and forming itself as it goes along.
What this means is that your particular wiring diagramme is 100% unique. Not just where a specific nerve lies along the path from brain to hand, but the specific pathway itself within the huge bundle of nerves that fans off from the brain stem. And it's not just one nerve handling a complete, yet complex action. It's scores and hundreds of fibres that all have to coordinate within time and space to accomplish a specific action, and each of us does that a little differently.
There's just no way you can "send a wireless signal" or something and expect to get a coherent set of actions. You would literally need to send billions of test signals over thousands of potential nervous pathways and in myriads of combinations in order to get the right combination that will cause a small flick of the index finger. You'll need to repeat the process millions more times just to get a slightly different flick of the same finger! Repeat the process billions or trillions of times to get all the fingers to flick.
What you've seen with those diode things is such an overkill. In medicine they're called "nerve stimulators" and are used to determine if a stringy bit of tissue is a nerve or something else. Blasting the tissue with an electric current will cause muscles down stream to "twitch". This twitch is just a chaotic, disorganised contraction of relevant muscles.
This is the equivalent of having someone lie down by smacking them with something the size of the Moon. Those devices can not cause muscles to perform the ultra refined motions required to pick up a bow and play music on a violin. Even if you had enough devices to control each muscle, and could figure out where each specific nerve pathway is for a test individual, none of that knowledge will be directly applicable to another test subject. You'll have to go through the same process of determining which nerve is attached to which muscle.
REALITY CHECK
Not feasible with current technology. And furthermore, not even practical with any foreseeable technology.
Maybe someday, but I think you'd need a way of sending micro-focused signals that are shielded and waveguided: you'd need what is basically a truly wireless wire, a signal whose orientation & location within space and time can be freely manipulated. And you don't want any unintended targets to be affected. And you'd also need a way to home in on a specific micro-location within the victim's body so the distal end of your waveguide can "plug in" to the victim and then you'd have to be able to anticipatorially control the connexion points within time and space remotely and perhaps even without even being able to see the victim. (If they throw a poncho over themselves, you're not going to be able see where exactly your connexion point is in space.)
All that in addition to creating some kind of AI that can near instantaneously scan a body at the submicroscopic level, determine all nervous pathways and their connexions within the brain and the body, download from the brain all the "muscle memory" algoriths that actually do the work and determine appropriate external interfaces that will mimic all the brain-muscle communication structures that would normally arise from within the individual.
Frankly, I think it would be much easier to just say MADGYCKQUE! and have done with it!
