There is NO reason to euthanize your rooster if you love and want to keep him, as long as you are able to provide him a little extra care. And it does sound like you are willing. He can and Will absolutely recover and regain the ability to participate in and enjoy normal chicken behaviors. There are threads here on byc where birds have done so, & there are also videos on the internet. He is no longer perfect, but if you feel his life has value, then he is still good enough.
Gimme a minute, I'm going to provide you with links and videos of birds that lost their feet to frostbite, yet recovered not just to survive, but to thrive. Not only chickens, but parrots, hawks, etc. I understand that not everyone would put forth the extra time and care to help a handicapped bird carry on, but since you are willing, I assure you that your little rooster is able.