If this is pre-WNM, neither Rand nor Chapel should be present. Rand was presented as a recently assigned captain's yeoman in "The Corbomite Maneuver" (which is the real beginning of the season despite the recent DVD set's bizarre decision to arrange it in airing order), and Chapel only came aboard to search for Roger Korby. Well, I guess maybe one could stretch things enough to justify Chapel being on board for a year or two before "What Are Little Girls Made Of?" though that wasn't the impression I got from the episode. But having Rand aboard would be a mistake.
But then, having Chekov aboard would be a mistake too, since he'd still be an Academy cadet at this time. I'm hoping his role in the film is fairly minor and peripheral, that he isn't actually serving on the crew yet. Maybe there's a sequence that takes place at the Academy and Chekov is a student who gets caught up in events.