Don't worry. Be happy!!!
We just got off the Western Cruise this past week and we had a private excursion booked for 8:30. We made it to our destination by 8:00 AM.
If you are not on a Disney Excursion, you go to the Walt Disney Theatre at 7:30. Your entire party must be present. They then give you a ticket. On our particular day there were only about 60 people present at this time. We were then escorted to the tender boat and were on the first one.
I could be wrong, but to me it looked as if people who booked through Disney were on a totally different tender that went out the Aft of the ship. We were never with Disney Tours. Those who booked private tours or just wanted to get to the Island, left through the front of the ship.
The tender ride holds about 100 people I would guess. It took about 10 minutes. When you get off head up to the dock to the street. If you need a cab, turn to your left. Walk over a small bridge and there is another dock like information building on your left. It was here that we found all the taxi's. We just went to the first one in line and off we went. People going to 7 mile beach paid $5.00 US each. We paid $6.00 to get to the Yacht Club which is a little further.
Good Luck
Kim