You do NOT need the EMP, but it is the easiest way to kill the electric zombie. The galvaknuckles are probably more useful for this, especially since they help when running to the cornfield.
Also, there is a way to force the electric zombie to appear, instead of waiting for it like this guide suggests.
-Turn the power on (and then turn it off)
-Wait until it is storming directly above you (I think the storm rotates throughout the entire map)
-Kill the last zombie to end the round WHILE it is storming
-The next round should start WITH an electric zombie near you (We tried this 3 straight times last night, only getting to round 3 or 4, and an electric zombie appeared every time)