As I posted in another similar thread....
IMHO the solution is:-
1) REMOTE SHIP TRANSPORT
We get the planned mechanic of being able to request a remote ship is shipped to our current location. This is done via a transporter, and takes a realistic amount of game time.
So if it's X hundred light years away, it may welll take a few hours of game time to get the ship to your current dock. So should you request this and leave the game. On your return a few hours later, your other ship will now be available.
An uber nice touch would be to actually be able to see the transporter turn up at the station at arrival time, and for your ship to go into the station.
2) PILOT TRANSPORT
Using the same system, you book your current ship (and you) to be transported to another station. Again this will take real game time. Ideally you'd do this request before leaving the game over night or something.
If you decide to cancel mid-transport, you're left in an appropriate system enroute just as if you'd jumped in, ideally seeing the transporter hyperspacing away.
To aid game mechanics I personally don't think you should be able to book transportation to a station you haven't previously been to. Use a hand-wavium of some form of registration at the station or something.
ps: NPC characters simply flying your ship is an even simpler explanation than using a transporter! But I think it would be cool seeing these transporters arriving at stations delivering and taking ships away.