The only birds I've despatched so far were our ducks. I would've loved to have kept them, but we had geese we got at the same time (from the same farm) and the geese hatched out some goslings. The drake was always a bully to the geese (who I vastly preferred over the ducks) and started going after the goslings - that was the final straw for me.
I locked up the drake to let him clear his bowels, but then the remaining duck freaked out when she realised she couldn't find him, so I made the decision to cull her too. It felt wrong to have a single of any species (with an exception reserved for my dog which may also be wrong, but given she doesn't really like other dogs I have my justifications for it).
The day of the cull, I cut the end off a feed bag, fed the drake's head through the opening, and just stared at him for awhile. It was the calmest he'd ever been. He just sat there, checking out the world while I had him in that bag. No fighting, no signs of stress or concern. The whole thing creeped me out. Here was this creature that, while terribly cute, was also terrorising my preferred livestock and was at least a contributing factor to the loss of every single gosling that hatched out. I stared, and stared, and stared and then, at some point must've been at least 15 minutes later, I realised that I wasn't going to let him go back to terrorising my geese, so I had to go through with it.
I tried dislocating his head from his spine with a sharp pull. But I also don't know that I did it well enough, so immediately picked up the axe and put him on the block I'd preprepared and chopped his head off. The duck was actually easier. I don't know how these things work, but I worried she'd smell the blood and the death and understand her fate so I was compelled to just get it over with as quickly as possible as a sordid kindness.
I cleaned them out quite quickly, but it took me hours to pluck. I just kinda oscillated between not knowing what I was doing and also just feeling bad about taking another animal's life. It was a sad day all around.
I am pretty pragmatic though. I'll worry about something until it happens, and then when it happens I drop the worry and simply respond. No use carrying on about something that's in the past. I also knew if I wasted that meat we'd have to buy meat from somewhere else, and I could all but guarantee the quality of life would have been much worse for whatever meat we bought. I didn't think twice about eating them, and they were delicious. Just getting them into the freezer was much harder than getting them out.
I have since convinced my husband that we should start our own self-sustaining dual purpose flock. So while the experience was sad, we can assume that it wasn't traumatising - at least for me.