I never heard about the baking soda & vinegar method until today. I am going to use that method if I have to cull again.
One way we used to cull chicks, and other small animals--sad, but necessary sometimes....
We would put the animal/chick in a brown lunch bag, and gently fold it up. Then put the bag on the sidewalk, and drop a very heavy block or brick onto the bag. The animal never knew what happened, and it died instantly.
I used to do this when my father trapped mice and lizards in those sticky traps. I hated to see them suffer there in the glue, starving and dying of thirst. So, in the bag they would go, and in a second, the suffering would be all over.