We've witnessed many weddings at CSA, and we will be doing our vow renewal (15 yrs) next summer. The ceremony on the beach will feel quite private and personal, even though you will see other guests around you. The 'alter' is set forward from the chairs, and they make sure the beach is clear in front of the alter towards the beach. Most guests will try to stay away from the area when it's obvious that a wedding is about to take place. Aside from that, just know that everyone is smiling and happy for you as you get married in the most amazing place on earth! If it's very important to you that you see noone during the wedding, you would do better in the garden - it is very pretty, and very well kept (in spite of what you may seem to have heard), and very private. Honestly, I wouldn't pass up the chance to have the wedding on the beach!
We got married on the beach and honestly didn't notice anyone else around us during the ceremony. People are very respectful of the moment. It was really the best decision we ever made as we were blessed with a gorgeous morning. I hope you don't change your mind.