The only known way to send an electrical attack through the air in any controlled way is with an electro laser. Basically, this means you creature has hand organs that can create very brief but powerful laser at its victim to create an ion bridge to conduct the electricity through. For this to work, the ionization has to be more conductive than the environment to give the shock a controllable structure to pass through; so, your creature's fur will need to be resistant to electrical currents.
That said, you do not want it to be resistant to currents where you want to be able to touch shock.
To this end I would go with well hair: Hair itself is resistant to the flow of electricity, but the oils and moisture that builds on hair is conductive. So if your creature has no sweat glands in its hands and feet, but has sweat glands elsewhere, it can make it's hair conductive on places it wants to touch shock from, and prevent your electro lasers from running down your body and out your feet.