There is - or at least there was, 20 years ago when it was my job to know such things - a federal law which allows a person to transport firearms through states, "...if possession of the firearm by the individual is lawful in both the state of origin and the destination...". I, too, had to pass through New York State en route to Ohio, but I felt relatively confident that there would be no problems if -
A. the firearms were unloaded, in a secure and locked container, and in the trunk;
B. I drove in a manner which would not cause an officer to stop me;
C. ammunition was in a separate container, and not in magazines or speed loaders;
D. I reviewed the laws of each state through which I would pass before my trips.
Now, item D above is the difficult one, but today's Internet allows information to flow. I recommend going to each state's web page and reading the applicable laws directly. If that is too daunting, the NRA has information available, and I believe the U. S. Concealed Carry Association [USCCA] offers a similar service. I suppose that carrying a tested container of powerful pepper spray on your person is an alternative, but I always relied on that as merely a back-up.