From the Sussex ordinances found here:
9.01 DISCHARGING AND CARRYING FIREARMS AND GUNS PROHIBITED. No person, except a sheriff, constable, police officer or their deputies, shall fire or discharge any firearm, rifle, spring or air gun of any description, bow and arrow or sling shot within the Village or have any firearm, rifle, spring or air gun in his possession or under his control, unless it is unloaded and knocked down or unloaded and enclosed within a carrying case or other suitable container, provided this section shall not prevent the maintenance and use of duly supervised rifle or pistol ranges or shooting galleries authorized by the Village Board except as herein provided:IANAL, but as I see it, both ordinances are pre-empted so as long as there isn't a school zone issue, you should be good to go.19.18 USE OF FIREARMS AND FIREWORKS; HUNTING WITH BOW AND ARROW; TRAPPING. No person shall carry, fire, or discharge any gun, pistol, or firearm, nor shall any person hunt with bow and arrow within any park or parkway. The word "gun" shall include air gun. No person shall discharge fireworks of any description except with permission from the Board.