In NJ, can you send a demand letter for a monetary judgment already awarded by the court?

I was awarded a $1200 + $22 court cost judgment by default about 2 months ago. The man has refused to repay me by amicable means. Could I start my judgment collection by sending a demand letter, by certified and regular mail, to both he and his lawyer? I would like to avoid all other means of collection at first, but I feel like they are unavoidable. Is a demand letter a good place to start?