which type of cable/wires do i need

I don't know what you have available, or how much you know about the wonderful world of wire, so here is a general-purpose answer.

The energy levels are so low that *almost* anything will work. For wiring to the switch, anything larger than #30 (30 gauge, or 30AWG) is ok. Even #30 wire-wrap wire (very thin, solid, plated wire with Kynar insulation) will handle the DC current level, but it will have a problem. #22 or #24, solid or stranded, are typical for this kind of application. Solid is better behaved for internal wiring (no vibration, no repeated flexing).

For the wires out to the handles, stick with stranded because of the flexing involved. Lamp cord (#18 pair) is overkill for the energy level involved here, but rugged, available, and cheap.

As for that "problem" mentioned above - frequency response. I completely disagree with the folks who claim that the reason lower frequency zappers appear to "penetrate" better is because of "skin effect" in the human body. However, when it comes to the circuit wiring of a zapper and the wires out to the handles, skin effect is a valid concern. I don't know how much techie detail you want, but, basically, as the frequency of the current flowing through a wire increases, the apparent thickness of the wire decreases. So even though the average current flowing through the switch is well within the current capability of #30 wire, the performance of the circuit at those higher zapper harmonics (500KHz) will be degraded. This is even more true with the longer wires going out to the handles.

There is a trade-off between the increased skin effect of small wires and increased inductance of fat wires. Both are bad in this application. Without running the numbers, my guess is that #22 stranded pair is the best, if you can find it. Having the two wires close together is better than having two single wires widely separated. One approach is to take two pieces of #22 and twist them together *loosely*, one twist every 3-4", to the point where they separate out to the handles.

Litz wire would be best, if you just happen to have an RF research facility in your pocket.

ak