You can switch your weapon as many times as you like. When you get to the "first list" (6 total calls), you can fork over things from that list, and when you get to the "second list" (6 more, 12 total calls), you can no longer fork over things from the first list, but you can fork over things from the second. Despite the fact that some second-list things have worse stats than their first list counterparts (great katanas for example), they still work better for the NPC. Illogical but true.
Say I'm on the second list now, and my NPC has a great katana from the second list. I can give the great axe from the second list, play with that. Decide I don't like it, try a great sword. Decide I don't like that, give great katana back. You can change weapons as much as you like - there's no limit, other than the fact that you don't get any gil refund for buying the equipment.
Your NPC starts with first-list sword and first-list shield (namely Xiphos and Lauan Shield). If you intend to stick with that, then you don't have to do anything when you get to the first list because your NPC already *has* that stuff. (Just like you don't need to do anything to change your NPC's attack style at 3 calls, if you want Shield - the NPC is *already* Shield, so you don't need to change anything.)
If you give your NPC a 2-hand weapon, and then give your NPC a 1-hand weapon ... they no longer have a shield (they lose it, when they get a 2-hand weapon, for obvious reasons). That's why you can give your NPC a shield in the first list, so they can get it back. And as for the second list, naturally if you can give your NPC a shield like any other hand-equippable item, you can give your NPC a better shield (Shell Shield if y'all are wondering) just like you can give your NPC a better 1-hand weapon.
This has always been an option, it's just that since the first dialogue for changing weapons was heavily leaning towards *weapons*, nobody thought about shields. Second dialogue mentions "weapon or shield" and people went "wha-huh?".