This probably won't help because I don't know the laws in NY but here in KY it is legal to keep a gun in your glove box (w/ or w/out a CCDW, locked or unlocked, loaded or unloaded). NOT in the console/armrest though. So arming / disarming would take place inside the car, or you could just keep it on you while you drive (I don't think there is law against driving armed here).
Before I finished this post I found this regarding NY state gun laws... not easy info to find (click quote to see where I found it):
"Possession of any "loaded" rifle or shotgun in a vehicle is illegal. A loaded handgun may be carried in a vehicle by a properly licensed individual."
From what I read it seems that in NY, in most cases, the license to OWN a gun also serves as a license to carry it.