In more realistic scenarios, "down" is just defined by the direction of thrust. So approaching a ship, they will be down assuming you are decelerating to match their velocity, but they will be up if you are still thrusting towards them.

But all of that has almost nothing to do with how people will think of orientation to other ships since generally speaking you won't be using eye sight to communicate ship to ship. At that point an agreed upon down will be needed. Probably aligned with galactic or star system to establish a plane, and probably right hand rule to establish up and down. In general given that space is big and ships are small they will just be points on each others radar until they need to dock with each other so it doesn't really matter how people are actually oriented, as long as when they communicate what they say makes sense to the other side.

edit: or maybe down is towards the currently orbitted gravity well, like towards a planet/moon/star.