Very good post.!!!!Oh, I sure know where you are coming from. It's been a very, very hard thing for me to do. Re-homing isn't the answer--why should you give away all your hard earned work for someone else to slaughter (who might not do it kindly). The kindest thing is to do it yourself.
Reading is a start and is a good way to decide on what method you want to use, but YouTube videos are a much better learning tool.
Choose the method you want to learn. When you choose the method, also evaluate how much error there might be and what that error would be. Chopping off a head with an ax is pretty quick and clean but there can be a lot go wrong. My avian vet dislocates their cervical spine when he processes chickens but I am pretty sure I would not be able to dislocate the spine quickly enough or with enough force to finish the job. I've thought about the broom handle method. I've thought about shooting the bird in the head with a bb gun. Pithing is pretty exact, so not the method for a novice with no one to show them (in my opinion). I finally settled on slicing the carotid arteries.
If you are going to use a knife, it has to be really, really sharp. Also, make sure it is long enough. I think the knives I've bought are a bit too short. You need to use a lot more force than you think you need. Being timid only makes it a longer, more stressful process. A couple of other pointers if slicing the neck is to pull the skin really tight--if you don't you won't get a deep enough cut. You want to make one cut deep on one side and then quickly do the same on the other to get both carotid arteries. The carotid arteries are the arteries which feed the brain, the jugular vein takes the blood from the brain to the heart. If you only go deep enough to get the jugular, the fresh oxygenated blood will still be feeding the brain and it will take a long time for the animal to lose consciousness from lack of oxygen to the brain.
If you are going to use and ax practice, practice, practice. Use a stick and practice chopping it completely in half--you need to know how much force (more is better unless you lose control) and you need to be accurate. Most people use a wide hatchet.
Learn what a dying chicken looks like. It's not pretty but it is better to be prepared. I think a decapitated chicken struggles more at/after death than one that is bled out, but I've never decapitated one so I really don't know from my own experience.
The actual cleaning of the bird is not hard nor is it very upsetting. I, and I think others on this thread, found the actual killing to be really hard to do emotionally. Watch a lot of YouTube videos to learn how to kill and how to clean.
The day you are planning to process this bird, be very prepared. Know exactly what you are going to do. Have everything you need on hand and ready. Have a book open to the pages on cleaning for reference because you will forget something. Know that there is a skill to doing this and you will not be skilled the first few times, but work really hard to make the kill quick and stress free. You can do that the first time if you are determined--just keep in mind you can't be timid. Timid is what causes most of the disasters. Timid, dull knives and poor aim. You don't want to be going back hacking away at the bird.
Do you know how you want to dispatch the bird?
If you want to learn how to do it from a person, you might try contacting a high school that offers some agriculture classes. The person running that program might have some suggestions. Four-H Clubs might also have someone who could help.