The most authoritative answer would likely come from NY DEC. Have you inquired with them? Doing so in writing would be advisable for any future legal situations.
A knowledgable second-hand source would be NYTTS:
http://nytts.org/
NY State sure doesn't make the legislation easy to find. It looks like only
Chelydra serpentina is regulated, so all other species of snapper are either unregulated or covered under some other law that I couldn't find.
https://govt.westlaw.com/nycrr/Docum...efault)&bhcp=1