I believe that as long as you do not actually accept a mission from the prince, you can just ignore him and go off and do other missions and then come back and accept it later whenever you want. At least that’s what I did. After you accept a mission the timer starts ticking to complete it on time and if you don’t you’ll get dinged for rep.
The game is designed to be played either as a sandbox or to complete the story, however you want to do it. If you want to just freelance it, then I’d suggest completing the initial mission to transport the Arbiter because that’s a quick, easy 10,000 credits. After that just don’t accept any offers from the prince and instead go off to other sectors and trade or do whatever you want. You can look at the missions the prince offers, just don’t accept any.