I wholeheartedly disagree with shooting the cat. How can you be so sure it is a stray and not someone’s beloved pet?
Killing an animal out of defence should be a last resort. There are so many things on the market designed to ward off predators eg anti climb spikes/paint, noise emitters etc. That shooting first is just silly.
Cats are difficult to restrain, they often love to be outdoors and then keeping them in your property alone is not something you can do.
You get indoor cats that don’t go out, but mostly they will and once out we have no control over them.
I’m sorry the cat is attacking your flock. Why don’t you try feeding it proper food and then taking it to a shelter? Posting online to make sure it is a stray? Granted this all takes time but what’s a bit of time worth when you’re not destroying a creature of this planet.