As stated above, processing is my least-favorite bird-related task. The first time I was very emotional and it was hard for me to see the life going out of the bird's eyes, knowing I did that to him. The way I get through it is this:
Chickens are killed by the millions every year around the world, so that people can eat them. That is just a fact. What is also a fact is that 99.9% of those chickens live horrible lives. They are bred specifically to be raised for meat and live in large warehouses, where they sit around and do nothing but eat for 6-8 weeks at which time they are killed without humanity.
Another fact: while 50% of chicks hatched are male, only a fraction of them ever have a purpose in life. For fertility you only need about 1 rooster for every 10 hens but many people either choose not to or unable to have roosters so that means even less available homes for roosters.
So....having excess males is part and parcel of this hobby/business. When I have them, they are raised in humane conditions. They not only have free access to good food and fresh water but to grass and bugs and sunshine. They can stretch their wings and fly (as well as their heavy little bodies will let them), and dust-bathe and enjoy the companionship of their flock-mates and their people. When the time comes that processing is inevitable, I do it quickly, humanely and with respect. They are treated kindly and gently right up to the last minute.
The method I use doesn't involve tying them up by their feet or putting them in a killing cone. Instead, I wrap them in an old towel to contain the wings from flapping, and tuck them under my arm. I sit in a lawnchair and hold them for a few minutes, talking to them until I feel them relax. While I am doing that, I stroke the neck area and tap gently over the artery in the neck. This gets them used to the sensation and also helps me to feel for it. My pre-sharpened knife is then used to slice very quickly and cleanly through the artery. You know when you're cutting vegies and you slice your finger and you see blood but don't feel any pain yet? Well, it does take a few seconds for the message that there is pain to be felt, to be sent to the brain. During those seconds, the life is draining out of the bird. About the time the message is sent back "Ouch, that hurt", they are already losing consciousness.
The freakiest part comes up to a minute later, when it will feel like they are struggling for their lives. Despite the towel holding their wings in, the death throes can be so violent that it can be hard to hold onto them so it is good to know it is coming and be ready to hold them tight. At this point, despite how it feels, they are gone and oblivious so don't let the thrashing around make you feel bad that they are still aware of what is going on, because they are not.
If you haven't already, I would really recommend looking on YouTube for some videos. Before I had to do the first, I looked at a bunch of videos and made my own cone out of an old plastic bottle. That worked fine. But then I came across this:
and I really liked her method, so adopted it. Every bird I've done since then has been done using this method. I have never processed a duck or goose but I would guess the anatomy is similar enough that the same process would work (although a goose might be too large to hold under one arm?) The only other hint I can give is to make sure the knife is super, super sharp. The only thing that makes a distasteful job worse is to try to do it with a dull knife and feel like you are hacking away at them causing them to suffer. Good luck and please, let us know how you get on?