Most transatlantic cruises include air fare. Ask your travel agent at time of booking if they can delay your return flight. I am sure this can be arranged but you will need to arrange this at the time of bookin.
All the agent has to do is deviate your flight to when you want to come back , some cruise companies charge for this , this generally has to be done at the time of booking though, also bear in mind hotels in nyc are expensive . Michele.