Might look into why this chicken is being loud. It's not normal for them to draw attention to themselves. Maybe needs some alone time with a rooster, you do have a rooster, right?
Don't think shocking the bird would be safe or effective, since your device would need to be close to the skin, and don't think feathers conduct very well. Burn pretty good though. Little watch battery wouldn't last long either.
Get a rooster, which of course would be much louder, but the hens much happier, and better egg production. Could always hang a frying pan next to her coupe.