"Prove it, then - gimme the gun & another silver bullet."
You just got to wait and see if any townsfolk die the next day.
If silver bullets are required to kill werewolves, what did people do before there were guns?
I think as long as you use any silver stabbing device, you'll be good.
Bullets are just the most efficient method of long range delivery.
So what happened prior to 4000BCE?
It's not the bullet, it's the silver. A silver knife would also work, but you're way more likely to get mauled in the process.
Oh, and also the projectile from a sling is a bullet, so bullets may be older than the concept of werewolves. (It's hard to be sure, because they also predate written language. Not to mention metalworking.)
"Are you a werewolf?"
"No? He is, which is why I shot him."
"Prove it, then - gimme the gun & another silver bullet."