I've got axes, hatchets, machete, saws, knives, etc in my SUV at all times in NYS.
All used for trail clearing and whatnot, nothing nefarious or with any other intent. And that's kind of what the law states, intent of use.
But if it looks like a weapon you're probably going to raise some suspicion.
And I'm a long way away from NYC but I would clean my vehicle completely out before I crossed those borders.