It's really not that hard. It's their life purpose to be food and to feed the garden. I watched a video from the guy that runs the Farmstead Meatsmith, and he went over how to kill food animals in accord with their species. Rabbits usually go fast from a calm place, so I like to comfort my animals before the harvest. They don't know what hit em, and if they struggle a lot beforehand, I know it's not their time. The stress of the struggle and fight can flavor the meat, so I give em a.couple days after that. Spend more time with them and get them comfortable with me being around, so that the next time they're more open to being handled and comforted before the one savage instant.
The process is to get em comfy in my lap with my right hand underneath supporting their hind legs, with my left hand on their back behind their head. In a smooth movement, I close my hand around the back legs and around the neck, tipping the head back and pulling the back legs. The neck pops and it's over before the rabbit knows anything weird is happening. Naturally, that's how they'd go; with a quick strike from a bird of prey, or from a snake or carnivorous mammal. No struggle, quick and painless, so I try to honor that.
My friend lives out in the country where they're allowed to discharge firearms at their home, and he gets the animals comfortable and pops em at the base of the skull with a .22. It's fast, but that's loud and ammo is expensive. Plus, I actually enjoy the sacredness of my process. I handle the animals pretty much from their first day, so to take on that role of apex predator feels right to me. I think it was Daniel Vitalis that called it conscious omnivory. I've always liked that wording.
I'm glad you see the sacredness in it and are conscious about it. I wish that was the case everywhere.