Neil,,,, that October class will work just fine for you,,,,,,,, the Long Island small game season doesn't open until November 1st :)
See,,,, and you thought you were gonna miss it..... :)
BTW....... you're not gonna find much in the NYS Environmental Conservation Law regarding airguns and hunting small game with them,, it just isn't there. My friend, who is the DEC Lieutenant in charge of the Eastern Suffolk zone explained to me that hunting small game with air rifles is legal basically by "ommission" in that air rifles are not specifically mentioned as legal small game hunting tools BUT they are not listed as being prohibited either . Hence,,,,, they are legal basically by "ommission" from the law.
Considering that this is just "how it is" with respect to the DEC hunting laws don't go crazy over researching it,,,, it's best to just take it and run with it.... it's legal so when the season opens lets go hunting :)
Hope this helps you out......
Jeff