We are all going to reach deep inside at moments like this. The tools we bring to the task are bundled in our own experiences and emotions. My personal inclination is to avoid beheadings due to bad experiences with that method. Just my experience, I won't try to discourage those who have had better luck with it, just be honest about my experience. We are all talking about something we don't WANT to have to do. For meat making, I found the kill cone and some careful anatomical info to be a revelation. It really worked as advertised. Not sure I would have allowed the chickens in the door otherwise.
When I say personal experience I am not talking about an animal I killed in the freezer. I haven't had to do that yet. I was talking about the physical experiences I have had with hypothermia. Not an imagined fear - actual personal, multiple experiences, wet, dry and and varying temps.
Less direct but just as compelling is evidence I have seen in the wild. Animals who slowly die of cold don't show signs of distress. Of COURSE a critter that falls through ice into a pond is going to experience panic. But a reptile, bird or bat caught asleep in the wrong place at the wrong time just goes to sleep, permanently. I list those because they are what I have experience with. You find them roosted, curled in a nest, out on a rock, it just looks like they are asleep.
If I were a little mouse or bird and had to choose, put me in a box with some bedding to slow the temp drop and put me in the freezer.
I hope this is an informative digression, not the start of strife. We all have to do what allows us to live with ourselves later.
Hugs to the OP
with a flute
with a flute