My Wife and I ussually go to CTI in mid July and the water temp there is ussually high 80s to low 90s. if you check out the tropical weather at accuweather they have satellite maps that will give you the water surface temps. Right now it looks like it is mid 80s. Don't forget though if you dive it will tend to be about 10 degrees cooler past 60ft.
I can't speak to CSS.. but CSA (on the other side of the island) in September is beautiful. easily over 70 in the mornings. It's not cool, that's for sure. (That would be my trip to Nassau in March. After you got in it was fine...but at first..... COOOOL)
Not sure of the exact temperature but you certainly won't be feeling chilly when you get in, nor will you be feeling overly warm. It's just perfect. We spent much time just floating and loving every minute.
From now til Sept, water temps in the ocean should be in the mid 80s. Storms and heavy rains can temporarily change that. Off Sunset Beach, the White River meets the sea, so those water temps are mixed- I'd say mid 70s to 80 and up. Depends where you stand!