Do rematches against Shadow Pokémon change the Pokémon's nature?

I want to catch Croconaw with a favorable nature in a Dive Ball, and to make it easier, I want to transfer the Smeargle I use for capturing from Pokémon Emerald with the Dive Ball since it can't be purchased in Pokémon Colosseum. My question is whether Croconaw, being a rematch, will have the same nature as the first time I saw it, like a roaming Pokémon that doesn't change anything no matter how many times you encounter it.