Have you considered entering the bank at Gun Cay? It is a pretty sail, and many things to see on the bottom as you traverse the bank. Then you can anchor at Chub Cay and enter. Then sail around the Berries, and head north.
At the Gun Cay entrance you can check in at Cat Cay, but they wanted $100 to tie our dinghy to the dock. In Bimini they tried to force me into a slip to check in. I told them I was on the go, and leaving as soon they would do my paperwork. Took 30 minutes to do it while I anchored off the north end of the docks.
In Nassau when not picking up family &, or friends I anchor, and climb the wall at the customs house where the cruise ships are. If I am meeting people I get a slip to make it easy on them. When I get home to the boat tonight I will look to see what cruise book I use. Have fun, and be safe no matter which way you go..............