I am going to go against the grain on this one. Put her out of her misery. If she is blind and has already been ostracized, she is fair game for any of the rest of the flock. She will have hard time finding food and it just sounds to me like a bad way for her to try going on. Be humane and let her go on to greener lawns, if you know what I mean.
As for the 'man' bird. Lock him up for a while then watch him closely.
I know it is hard, I have had to put down some of my favorite birds and rabbits. I had to have 2 puppies euthanized last summer that were less than a month old due to defects. It is not for the faint of heart, but if you are doing it for the sake of compassion, and you treat your creatures humanely, there is a time for everything.
I know I would hate to watch a creature die a slow death because they couldn't fend for herself.
I would use the ax. It is quick and even though they flop around afterward a bit. It will not hurt her if you are swift.
Good luck in whatever you decide.