We just got off the 2/2 sailing of the Dream and booked the Nassau Harbor Tour.
The 9:45 time is the time you will meet on the ship. For us it was in 627. They check you in there, give you a sticker with a character (we had Simba). Then they wait for folks to show up and we left 627 about 10:00. Then we were put into groups outside by character. harbor cruise and see and sea go to same boat dock, about a 10 minute walk with a
DCL guide, down the dock, through festival place where you can buy a water for $1, then to the dock where we boarded the Ballyhoo.
We boarded that boat finally and it finally left aboiut 10:30 or so, maybe later.
So no worries, the excursion time is the meet time, not the boat leaving time.