This is a frame challenge.
The answer would be pretty much any animal that ever existed, and any skin that ever existed on any animal.
Electricians use leather gloves when they handle high tension wires, for instance. The hide of animals. An excellent insulator.
Skin itself has a very high electrical insulating ability, a very high resistance. It is the pores in the skin, with sweat and such, that are the conductors.
Further, touching very high tension electrical wires is never a problem. Squirrels and birds do it all the time. Electricians handle live wires with thousands of volts potential difference. It is only dangerous when one is ALSO touching something else, that completes the path. An earth ground, for instance. If there is no complete path, there is no current flow, and it is the current flow that kills, not the voltage.
So basically ANY species "can grab and handle live electrical wires bare-handedly and be A-OK."