You'll have to move it miles away, FYI, if you can catch it. I'd rather not kill them either but once they get in the coop and find eggs, they'll be back.
The one that ate the ceramic eggs, the woman saw it leaving the coop when she was mowing. I had caught the previous egg thief and relocated it 12-15 miles away, but she is terrified of any kind of snake, and ran over it with the riding mower several times. That apparently wasn't 'dead enough' for her, so she got the hoe and attempted to kill it some more... but adrenaline being bad for fine motor control, it looked like someone plowed up a fair amount of ground around the carcass! Anyway figured might as well get the eggs back, don't think the snake would have survived them anyway.