Hmm, surprised I missed this thread. High Voltage was a specialty of mine since I was a kid. In order to safely and humanely kill a bird, you would need to charge up a HV capacitor of at least 1uF to 20KV. You need quick instantaneous power to stop the heart and nervous system. The vidoes are showing this done wrong as they are just cooking the victim.

You can accomplish this using a microwave transformer and rectifier diode plus storage capacitor. Not quite as high voltage, but still plenty. Best is to use a old TV horizontal transformer, oscillator, and rectifier.

The other problem is directing the current through the heart and preferably the brain too. Zap the brain and there is no suffering. So, wire at head level while feeding, screen mesh for feet.
If properly done, the horror will be the feet would be blown clean off. The bird will never feel a thing since it will just stop everything.

Horribly dangerous as all heck though. It will easily kill you too, so not the best solution.

Best solution? Stop using bird feed and the bird feeder, and start a seed plot with wildflowers instead. When I stop feeding, those nasty little buggers go away. I stop feeding in early spring so my bluebirds have a leg up And the house sparrows leave. I now only feed when there is snow cover or ice.