He can reclaim that at any time during this event just by dropping by the police station and asking for his weapon. c:

If he wants something stronger than that, he's gonna have to somehow show the Sheriff he's decent at shooting. The few extra guns they have which can shoot the special bullets are only actively being dispersed to the few people that a) his cops can vouch for, or b) he has actively seen shoot and has deemed a good enough shot that it wouldn't just be a waste of fancy bullets.