Why do you *assume* that the Vault Dweller had never seen a gun before? Your backstory is not forced down upon you like in F3. You could have been a Vault Dweller with a long military/police history/family an stuff.
The problem is your character in Fallout 1 had virtually no backstory at all. Sure, this leaves it up to the imagination of the player but that automatically rules out any possibility of a "right" answer.
Given what we know of Vault 13 however, it's unlikely that even if the Vault Dweller had a family with military/policy history they would have access to any sort of firearm. The armory didn't seem particularly well stocked, and I didn't see any sort of armed security force.
If the Vault Dweller was from Vault 34, my money would be on him/her any day.