I know Mimikyu has an exclusive z move and the box legendries do as well. Is the Mimikyu limited time and are the box legendaries limited time? (Solgaleo And Lunala in case you don't know what that means). I unfortunately don't have the games yet but I will get them in a few days.
There are no event z crystals yet for ultra sun and moon. The Pokemon exclusive z crystals are not event exclusive, so you can get them right in the games without connecting to the Internet at all
Note: You can get the Snorlium Z ingame as well