You probably want to do the sea trial with the surveyor - if possible check with to see if he would prefer to do that as a part of the survey. A good surveyor will want to be there for the sea trial.
Typically the surveyor will perform load testing on the engine, look at how thinks stretch & move under load, etc. The more realistic the better, so running the boat is a better test then cranking up the RPM''s tied to the dock. Also, the surveyor will check to ensure that things work in a "real world" condition, so there is opportunity there to test things out under way to ensure they work instead of just flipping them on dockside to make sure the lights come one.
There is a good article on sea trials recently published on Sailnet.