A shop won't remove the chrome. It's chrome over plastic. The chrome is so much harder. Media will blow through the plastic long before the chrome. A bodyshop will just sand down the chrome, prime with an 'etching' primer ... and fill the gaps. But yeah if you want it to be body color, that would be a good idea to have a shop do it. Esp if you don't have any automotive paints around (spray can paints don't come close). Like the above poster said, go talk to a body shop.
As I said before, you would be better off buying a black one (no chrome) and having a shop spray it (using adhesion chemical promotor for plastic). The extra work to prep a chrome-plated grille vs the simple prep on a black plastic grille would probably equal the price of a black grille. And the final product of a painted black grille will look better longer. The black plastic grille can be 'treated' with an Adhesion Promoter chemical which slightly softens the top layer of plastic and then they apply primer (then paint). The primer 'melts' into the somewhat soft plastic ...kind of like pvc pipes 'melt' together when you adhere them (very similar process actually).
The difference is huge: Using an Adhesion Promoter the paint is adhered with a
chemical bond (much stronger). Just sanding down the chrome and painting over it, is Mechanical Adhesion (much weaker).
Go talk to a body shop. Tell them what you want to end up with and what way you should go. Talking isn't going to cost you anything. Go to a good shop and tell them you want a grille that won't show rock chips for many yrs.
That's why most OEM bumper covers on cars can withstand years of rock chips and parking lot rash. When you see a bumper where the paint is peeling off in big flakes, chances are high it was replaced by a 'quickie' body shop and they just 'sanded' and painted an aftermarket bumper. They look good at first, but ultimately they don't last if not prepped properly. But some shops don't care.
https://www.ebay.com/itm/115172339156
good luck