The Zappy Hats are a type of weapon. When you use it, a shockwave of electricity will come out, dealing moderate to great damage depending on the quality.
The Electro Helmet is the middle tier of the Zappy Hat category. It can be purchased from Arms Dealer Larry at the Dangling Pianist for $18,550 ($9,275 if Discount Shopper is enabled), which is located on the 4th island. (Need Director's Cut.)
The Tesla Helmet is the highest tier of the Zappy Hat category. You can obtain it by maxing out the S.I.T. Professor job on the 4th island.