Yes, you will no doubt have port lectures for each port. While the focus will be more on shopping, there will be current information on the resorts that welcome cruise passengers. Like I said, the best beches are private. You can just hire a cab to take you to one of the resorts.
You don't seem to like the idea of ship excursions, but one of the best ways to enjoy the beach is to book an excursion that spends the day at one of the all-inclusive resorts. For a rather modest price (considering what you get) you are provided air-conditioned transportation, use of all facilities (beach and pool), and all food and beverages; really not a bad deal. You would probably spend more if you bought all these separatly.