It won't take you long to adapt if you consider that the civilian nuclear world is just that - civilian. Military solutions to military problems are appropriate, but fortunately you won't encounter any of those out here.
Your shift won't be comprised of twenty people who are simultaneously pursuing qualification on their own initiative, performing maintenance, cleaning the machinery, cleaning the toilets, standing their watches, and trying to fit sleep in when they can.
The people who clean the toilets don't operate the reactor. The people who operate the reactor will have a whole training department to support their career progressions as well as their continuing training. This department will also support the various maintenance and test shops - who also do not have to fit their jobs in between studying to operate the reactor and cleaning toilets.
Your shift will all be qualified to perform their jobs, which they will perform during their shift or turn over to the next one. Threatening to make them stay late will not have the same effect since they will be earning upwards of $50 - $90 /hr once they go on OT. They will also frequently have the option of telling you "no, I won't be staying late tonight" and you'll have nothing to do or say about it.
You won't be able to "win" a technical discussion by pointing out that your subordinate needs a shave or has sideburns extending below the tragus.
Your work will never be interrupted by something called "field day".
You can't make them come in on weekends or holidays or deny their vacation requests in order to "motivate" them.
There won't be a movie at 8 pm to entice them to rush through their work.
Quitting time is always quitting time.
Your operators will never be required to handle mooring lines, load potatoes, stand security posts, or run drills while they are on shift.
You will never run an actual drill on the actual reactor.
You and your fellow SRO's won't be studying how to shoot torpedoes, how to navigate the plant down the shipping channel, or how to track sonar contacts. None of you will be in charge of another work group that is totally unrelated to nuclear energy -- no torpedo, nav, sonar, or communications officers at a civilian nuke plant.
So you see, the use of threats or heavy-handed use of your authority, are just not necessary out here. Managers are problem-solvers. They enable and empower their employees. They listen, collaborate, and delegate. Employees are paid to do one job at a time, and they do it well when their expectations are clear and unconflicted.
You will find it much easier to supervise adults who are treated as adults. You'll find it not so hard to manage people when their work isn't a constant conflict between training, maintenance, clean-up, non-work-related duties, and sleep.
You are not the first, and won't be the last to make the transition from Navy life to an actual life. You'll get it.
Good luck, and thank you for your service.