Not to mention, in most states it is illegal to relocate trapped animals outside the property of the person who did the trapping.
That too and for good reason. I believe that even the Human Society frowns on relocation. Studies have shown the vast majority of relocated animals die from starvation, exposure or worse.....which for the varmints is a far worse way to go than some form of instant euthanasia. So in general, in many states, the law says kill it or release it and you do so on the spot. So it then falls back on how to do the deed.
I posted a rat killing video on a different thread.....one produced by the US Army and CDC back in 1950...........their trapper guy just bashed his brains in with a hammer. Highly effective......but perhaps not the best solution for everyone.