I am so sorry,
if your sure there isn't any hope for him to recover this to me is the best way to euthanize. I have used it a few times and even though it still wasn't an easy thing to do. For me it was so much better than chopping of their head and I couldn't do that anyway.
https://www.backyardchickens.com/ar...re-culling-the-injured-and-sick-babies.72140/
Again there are others on here dealing with frost bite with their chickens maybe join one of those threads.
https://www.backyardchickens.com/threads/urgent-frozen-feet.1288799/page-13#post-20907353 the thread I mentioned.

https://www.backyardchickens.com/ar...re-culling-the-injured-and-sick-babies.72140/
Again there are others on here dealing with frost bite with their chickens maybe join one of those threads.
https://www.backyardchickens.com/threads/urgent-frozen-feet.1288799/page-13#post-20907353 the thread I mentioned.