I really believe the best middle point between featuring a TIE fighter or a ship with hyperspace capabilities would be a TIE Advanced, like Vader’s in A New Hope. It’s recognizable and not that big of a strech as taking a regular TIE but renaming it TIE Scout.
I’m totally fine with the Imperial shuttle, though, and it makes sense in this film because the audience catches a glimpse of a wrecked shuttle in the Death Star scrap zone.