A few things I feel should be noted:
Any skill check to see if you have Catch satisfying rounds should be restricted by Lore. You have to know what rounds to have to have them (or know to use them).
A stunt that just lets you have whatever ammo you want is overpowered. It means that the creatures' Toughness powers are moot. No fair. He may not like it, but even the Sword of the Cross requires a Fate point and Sacred Guardian makes you take stress. These cost refresh (and Pure Mortals can't have them). -1 Refresh to potentially satisfy basically every catch is not balanced. Moving on.
If he wants to have the proper ammo (this is for in the middle of a fight):
Roll a declaration (Contacts, Guns, Resources, Craftsmanship) restricted/modified by Lore to see if you have it. It may be restricted by Resources too (if it's quite expensive). If it succeeds, you get the aspect "Catch Satisfying Rounds." You get a free tag for effect "I satisfy the Catch for this attack." After that, you'd be spending FP to keep it up (at least by how I'm understanding RAW).
Personally, if a character devotes a scene to preparing the proper ammo (still rolling a declaration) outside of combat, I'd allow him to satisfy the Catch for one scene. The difference here is that the character is prepared for ONE type of critter rather than ANY type of critter. He's actively satisfying the Catch and preparing, not just relying on a nifty stunt.
I'd make a stunt that gives a bonus to this type of declaration (pick a skill, obviously). If he's not confident he'll make the roll...too bad. He can spend a FP to declare (and it'll work for one attack with more FP being needed to keep it working) or spend a FP outside of combat in advance for it to work for one scene.
Remember, by satisfying a Catch, you're negating multiple points of refresh worth of powers. Examples within the system see this as costly (either in Refresh, FP, or Stress).