I just looked at the wedding pictures again to make sure that I remembered correctly. The beach was not that crowded, maybe because the ceremony was at 5:30 PM. There was quite a bit of space between the wedding chairs and the rest of the beach chairs with the towels draped over.
Just remind the photographer that you don't want other people in the photos if it can be helped.
My daughter and son-in-law wanted the ceremony and the reception on the beach, and the guys were all barefoot. The cocktail hour was on the sandy part next to the gazebo and the reception on the sand in front of the Gabi Club.They had a family friend perform the ceremony (which they wrote) and the judge performed the civil ceremony in the Romance Team office later. A friend of the groom was the emcee and the DJ just played the requested music.
I have to say that there is probably no way to eliminate the gawkers altogether, no matter where your ceremony takes place. January is high season and the place is packed with people.
Having said that, I also want you to know that you will probably be totally focused on the ceremony itself and your friends and family who come to share your day.