I have been on
Castaway Cay twice, first time on the Wonder and recently on the Dream, both times I went to Serenity Bay and both times the beach was almost deserted, plenty of beach chairs available.
Now, on the last visit with the Dream, the weather wasn't that good, most of the morning it was raining, but the air was still warm and the water was great. That time I had rented a cabana, as my uncle and aunt were with us and they didn't want to swim, so especially for them I think it was great we had the cabana, it was dry and the lounge chairs were much more comfortable than the plastic chairs on the beach.
So I think, if you want to spoil yourself, try to get a cabana, if the price is OK for your. They are quite expensive, after all. But I wouldn't say they are neccessary if you just want to stay away from other people, Serenity Bay should be big enough.
By the way, while I was able to grab the last cabana online on day 90 before the cruise, ours was the only one occupied on the day we were there, the other renters probably had cancelled because of the weather.
In March, we are doing another cruise on the Dream, then it will stop on Castaway Cay twice. Then, it will also be just my partner and me. Not sure yet if we should treat ourselves to a cabana for one of the 2 visits.