A "rifle" manufacturee and sold as a handgun is just a handgun. A "handgun" sized smoothbore is always a "sawed off shotgun", and you will need both NYS and Federal approval to own one.
It won't be simple, easy, rapid, or cheap. But if you are citizen and have no disqualifying legal issues (and I believe NYS still requires character references as well) then there is no valid reason for denial.
All else being equal (and it almost never is) bigger bullets tend to work better.