Hunting in NY is 12 and up. During the hunter safety course an 11 year old can attend but are not permitted to shoot a powder gun. They are restricted to BB guns that are spring loaded. 12 years of age and older are permitted and are required to shoot. In order to pass the Hunter Ed course, every one (11 year old as well) has to show safe handling of a firearm to the instructor. This is done during the live fire shooting in a hunter ed class. The instructor can deny any one that he or she sees not handling a firearm safely regardless if they pass there exam at the end of the class.
Hunter Ed classes that are not able to shoot do to location of class will do there field/shooting with a laser gun. The same safe handling of the laser gun is expected and as such if instructor sees poor handling of the laser gun instructor will deny there hunter safety certificate.
NY Penal law, age required for some one to handle and shoot a firearm is 12 and up for long guns and 14 to 20 for handguns. At 21 years of age and older one must posses a Handgun permit period to handle and shoot a handgun. Now you will need to look up definitions of what a firearm is and the definitions of firearm types.
Basically, a BB gun that is like your red rider that is spring is ok, but your pump and Co2 BB guns that use air are considered a gun and have to follow the age requirements for handling a gun. This includes air soft guns etc.