Once you get the bags off the belt and go through Customs, wouldn't you just head for the exit rather than the baggage recheck area? Grab a cart and place the bags so tags are face down or hidden from view.

If the skipped segment is the last flight on this ticket, that's all you'd lose out on. But as Ari said, if you have onward flights after that one, they'd be cancelled out. If you still need to get from NYC to your final destination, you might be better off to pay any change fee and just change the date to allow you a few days in NYC, rather than buy a new one-way ticket.