I believe POLAND_SPUD and a few others suggested I should've used a cheap RF circuit with an in-built controller for switching 12V instead of a doorbell circuit. Now that my trusted doorbell circuit is out of production and replaced by some piece of crap, I decided to buy one of these.
I've known about them for awhile as I've been tempted to use them to control LED circuits (which they are designed to do) but I never got around to actually buying one. I bought mine from deal extreme as I've used that site before and they have free shipping but they might be cheaper on eBay for some of you (plus, shipping is slow on DE; took almost a month to get here from the day I placed the order).
Anyway, it arrived in the mail today. It wouldn't work on only a 9V battery so I beefed it up to 14V (was easier then trying to get exactly 12V) and it worked great controlling a 12v computer fan. The dimming function would also control the fan speed. I could trigger it from at least 30m away, behind fences, or behind cars. I haven't yet tried it out on the stungun yet. There's still a risk that the stungun could short circuit and find its way to the 12v controller so I need to think of some good ways to insulate the stungun. Currently, my ignition circuit will short circuit when attached to the hybrid cannon if the electrodes are held too far apart; the spark jumps from the stungun circuit, through the bottom of its project box, to the cannon chamber, to the metal hose clamp, and from there either to my hand on the toggle switches or through the toggle switches and in to the main project box housing the batteries and other circuits. I've placed big chunks of rubber surrounding most of the stungun circuit but it simply sparks through any gap in the rubber (where the rubber meets the project box or another piece of rubber). Think I'll have to make a little rubber enclosure for it

TL;DR - If you want a cheap remote ignition circuit, buy one like this. All you need to do is wire your 12V batteries to one side and the stungun to the other.
