Verify the ordinance states "gun" which specifies explosive force.Firing a gun inside city limits, is, as I thought, illegal.
gun
/ɡən/ noun
1. a weapon incorporating a metal tube from which bullets, shells, or other missiles are propelled by explosive force, typically making a characteristic loud, sharp noise.
But arrows, slingshots and dart guns are fine. Air rifle maybe? Ballista? Catapult? Atlatl?
If you know how they are coming onto the property, install a snare.
Should improve your relationship with the problem neighbor if you are walking around armed. An armed society is a polite society.