So, progress thus far. I have wired the battery (rated 1500 mAh) and solar panel with one of the lights in parallel with the solar panel and battery of the other. With this power supply, I charged the modified flyswatter device. After an hour, I detected that the unit was about 1 degree Fahrenheit warmer than the surrounding surface, and all components were room temp to the touch. I left the device turned on for 11 hours straight, and the device was still able to produce sparks when the contact wires were touched. I still need to see if having it hooked up to an actual wire fence will cause more static discharge, but I think this system is actually going to be viable.