I am sorry for your little one.
Culling is not an easy choice to make and one I recently had to do for my one of my 3 week old chicks. Her leg was injured though not something she was hatched with. She had the problem for about two weeks and I tried many different things for her but nothing worked. It got to the point that she was a good half the size as her sister that was the same age and her foot was facing the wrong direction and she kept on getting stepped on by her brooder mate. My husband had to do it and he separated her head from her body. It was fast and painless for her.