That might work. The "cage" would be more like a sleeve in the region of the arm - just creeping out on the arm like a mesh tube (or even continuous foil tube) to protect the wires, electronics, and motors. A small hole would allow the motor hub to stick out of the cage, and the prop would be on top of that, outside the cage.

Heck, all the wires, electronics, and motors could be inside the "arm". Then coat that with some EM shield material (like a metal foil).

I like it.

Of course, from "like it" to "it's actually effective" there's still the nagging little field test to perform. It's the old shell-vs-armor game, since EM radiation has a penetration depth - Faraday cages are not magically 100% effective, make a thin enough one, and a powerful EMP would still do some damage inside. So now you need to carry thicker, heavier EMP armor.