Please don't shoot the cat! Animal control may not be much better since, at least here in Iowa, most cats that go to county pick-up or shelters end up dead anyway. But at least it gives her a chance.
There have been feral cats out here since long before we started having poultry and none has bothered any of the chickens, ducks nor, of course, the large and hissy geese. For at least the past year, a white-footed gray cat has meandered around the coops but has shown no interest in attacking the birds, most of which free range during the day when I'm home. She is the latest in a long line of apparently short-lived felines that prowled around without causing problems.