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Why have you opted to stay at EWR when your flight is from JFK? Personally I would stay the night in Manhattan, enjoy the city and then catch a cab to JFK. To get from Bayonne to Manhatten we caught a cab to Hoboken ($40) and then caught the PATH train over to 34th St and we exited right opposite Macys. A very central location and the PATH train cost $1.50pp. However, with your current situation you have no option other than get a cab, or a private limo or a shared shuttle (supershuttle.com) The problem with a cab is you will be charged double as NJ registered cabs are not allowed to pick up in NY (those are the states). It is like a cab from Yorkshire not being allowed to pick up anyone in Lancashire. So if you catch a NJ registered cab to JFK he will have to travel back to NJ empty.
Thanks for the very helpful comments. The cruise company booked us in to the Marriott at EWR as part of the package. I suspect there are several other parties who have the same problem as us. We had thought of forgetting the hotel at EWR and just finding one in Manhatten (where we have stayed before) making the transfer to JFK much simpler, perhaps that's what we ought to do. An added difficulty is that my wife is disabled and would have difficulty carrying luggage on and off a train. As an aside, although we thought the price for the cruise was very good value, we notice that the americam cruise agencies are advertising it at an even better price (putting on one side the airfare!).