First of all, consider the availability of the ammo. If a catch is +2 for availability (like cold iron, vamp weaknesses, normal silver), you can find it. If the catch is +1 for availability (like True Faith or inherited silver), you should not be able to find it; only a small group of people in the world should have it. If it was findable, it would not be rated +1 for availability.
Secondly, consider letting him make a resources or craftsmanship declaration to get the ammo at the beginning of a story, treating them as equipment. A serious gunslinger will start with steel-jacketed rounds anyway so no reason not to have the catch for iron at hand. Then against normal shapeshifters, one could make normal silver-jacketed rounds in advance as well with a craftsmanship declaration. Then load up with a few electrum or jade rounds if you are going against Greek or Persian/Indian critters in the campaign as a whole. Maybe add an anti-vampire paintball gun.
The IC justification for carrying all those types of ammo in advance would be a preparation or paranoia aspect or stunt. Your PC could well have been a boyscout before becoming a shooter in the know.
Third, keep the in-combat Declarations for unusual types of ammo. Remember that such Declarations need Fate points in addition to the skill roll.