Make USB keyboard wireless
You could try with something like this. If I get it correctly, it comes with power injector. Still, you'd need to connect the injector to power and that means wires.
I can't find any battery powered injectors at the moment, but you could always make one yourself. Still, it's going to be complicated and it's going to be a hack.
Unfortunately, as far as I can see, there's no elegant solution to this problem.