Back when I hunted the Southern Tier (DeRuyter area) in the '80s there was a minimum caliber, actually a minimum cartridge requirement for handguns!
If I remember correctly, the regs read 357 Magnum or larger (38 Special was illegal)! I don't know if this is still the law or not, but you may want to check things out in detail!
Another thing to check on, it was/is illegal to "go afield with rifle ammunition in your possession"!