I'm wanting to hunt for Shiny Buzzwole and Kartana but since I don't have the Ultra Sun version, I have to settle with the original one. But I don't know if they're shiny locked during the mission
No.
The following Ultra Beast encounters are prevented from being Shiny in Pokémon Sun and Moon, but are not prevented from being Shiny in Ultra Sun and Ultra Moon: Nihilego, Buzzwole, Pheromosa, Xurkitree, Celesteela, Kartana, and Guzzlord.
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