The real issue is what it can do to the public perception of hunters.

It doesn't win us points from the public if we do something that people will see as ruthless, heartless, etc. Try to imagine a five year old kid learning that their cat got shot when it was avoidable. That's a public relations disaster for all hunters and the kind of thing that makes people oppose hunting.

If you can get the problem resolved without shooting it, that's probably best. Sometimes it's not avoidable, especially with truly feral cats. Be discreet about it if it has to happen.