Regardless of your views on the discussion around police / police funding in America, when people think of New York City, the NYPD is very much NOT one of the first things people think about. I'm not certain if you are talking about New Yorkers, tourists, or people who watch Law & Order. There are just so many more things that people identify with New York. A police unit, which exists in literally every other city in the country is not what makes New York, New York.
Also, I'm not sure how much the East Rutherford PD or the New Jersey State Troopers that serve during Giants games would appreciate the team dressing up as police officers from a city in a different state.
I think you should try a whole different concept for the Giants. If you go the New Jersey route, please don't over do it on Italian tropes.