Moving out of nyc to nj.

No.

You are applying to be a citizen of the United States, not of the state of New York.

Since you finished the interview, you need to update your address with the USCIS and they will transfer your natz file to the appropriate field office, this will change your swearing in ceremony address. Use form AR-11.

From a practical point of view, can you wait 3-4 weeks? as that is usually how long it take to be scheduled and sworn in.