Might need to keep coming back to "there's only 85 people on board."
While Will Riker and Tom Paris were said to be extraordinary pilots, Star Trek seem to show that being able to handle a shuttle isn't really an unusual skill. Less piloting a high performance jet, and more just taking a van out of the motor pool. Chef might be able to pilot a shuttle.
The NX-01 could have NO
designated shuttle pilots.
I did say "might"
. With just 85 crew on board it is doubtful to have a non-com just there ready to fly a shuttle.
, looking at your departmental breakdown, you could save on a few positions if you removed the separate COB and made the most senior Non-Com hold that role in addition to other duties (like the First/Second Officers).
Likewise for the damage control specialist. Unless you expect them to get damaged a lot, lol. The Assistant Chief could cover this role, overseeing damage control teams and leaving the Chief free to focus on other matters in a crisis. Also to me just 4 general engineers seems a little light.
In Operations, the Chief and Assistant Chief could also be held in addition to other roles (eg one is the Shuttle Controller and another is the quartermaster). It would free up two more spaces for other crewmembers.
You could probably lose a communications specialist, four would be plenty (one per shift and then someone to cover the Chief when they are called away).
A quarter of the crew being scientists is understandable on an exploratory vessel. Given the importance of the NX-01 mission many would have multiple degrees/doctorates so you could in fact have more specialities covered.
Security could probably be scaled back slightly, perhaps down to twelve, giving you four per shift (including the Chief). They could then be on duty in the armoury when not training, running drills or security sweeps. All Starfleet personnel would be cleared for weapon use and basic self-defence, with others being better trained than others through experience. They would also work in tandem with Tactical, covering when/where needed.
These cuts would free up eleven posts, which could then be redistributed where needed. Just some thoughts though.