This is an essential issue for EVERY chicken keeper to address for themselves. No matter if you consider your chickens pure livestock or pampered pets, it is likely that you will have to face this question at some point in your experience. It's best to know just what you will do & how to do it well in advance of a crisis situation when you have an ill or injured bird needing a swift release from its suffering.
I agree that what is best for the chicken isn't always the least traumatic for the human owner, but it is necessary. I dislike dispatching my dear feathered friends in the same way I do my meat birds, but it really is the quickest & most humane.
I'm sorry for your dilemma, I pray for strength & grace for you to do what needs to be done.