ER & 44
The law regarding handguns is very clearly stated in the penal code. On the other hand I haven't been able to find anything in the penal code that supports the statements I've read (which you've repeated) regarding shotguns and rifles.
Believe me, I'm not doubting the accuracy of those statements (especially with respect to NYS) and would err on the side of not doing it. Having said that it would be helpful to know where in the penal code that restriction is addressed.
I'm a little surprised that given the number of times this restriction is repeated by various source that no one has been able to point to the section of the penal law that address this issue.