advised not to partake in the shore excursions and make our own way around
Perhaps they meant book your own tours instead of using the ship's excursion desk? Tours booked privately can often (but not always) be less expensive. If I had never been to the places you mentioned, I would not suggest you venture to far off the beaten path on your own. When a cruise line says the ship leaves at 4pm, they mean it. If you are on a ship's tour and it is late, they will usually wait. If you are off on your own, they won't wait. Actually they will want you back aboard 30 minutes prior to the departure time.