He doesn't have the authority to legalize prostitution. At most he can ask the police and prosecutors to ignore it. That won't keep the state police from being able to enforce the law.

The State of New York has laws against prostitution and does not have allowances for local governments to legalize it. The city however can ignore that it is happening and refuse to enforce the law. It then would be up to the state government to send in law enforcement and use state prosecutors to enforce the law. They probably wouldn't bother.