Personally, I think that it would depend upon what is actually involved in the operation.
The more involved the process, the less likely that I think your character would be able to accomplish it. The more steps or calculations required to enter hyperspace the less likely your character (unless he spent a LOT of time in the cockpit) would know what needs to be done.
I have read some stories where all that is involved is pulling up a menu on a screen and choosing the destination, while in others it involved lots of complex computations.
Also, being a passenger or crew member on a ship for 2 years has nothing to do with your ability to pilot the craft. You could equate it to working on a cruise ship or an airliner. Just because you are on the vessel, that does not mean you spend a lot of time in the cockpit, especially during the relatively few times that hyperspace would be entered.
Now, with that out of the way, let talk specifically about Star Wars....
From my understanding of the Star Wars universe, entering hyperspace isn't all that hard. For example, in the first movie, Luke has no starship experience at all. In fact, his only experience is with land vehicles (a land speeder). Yet, he is able to pilot an x-wing fighter without problem.
And in the second movie, he uses that x-wing to fly in hyperspace to visit yoda...
That kinda says to me that such systems would be heavily automated, so that a person without a lot of experience could activate them.