None of it is quick or easy, and it never is easy on the emotions, at least for me. But when it comes to culling, the bird is the number one priority, not how we feel. I totally get it, I can't take birds lives. I have a vet that studied avian medicine and puts them down for me. You might do some research on finding someone that uses sedation and then lethal injection to put them down.
The preferred killing methods here on BYC are the broom stick method or cervical dislocation at the head and neck...painless and quick. Lots of videos on line on how to do this.  There's the killing cone, bird is placed in the cone, they calm down with the blood rushing into the head and with a sharp pair of pruning shears cut the head off. Both of these methods are the most humane.