Walkers is very far north of the Bahamas chain and not much close to it.
The exumas are pretty popular for sailing as people will leave from Nassau to the exuma chain. The diving is pretty good there as you have some walls on the one side and more reef/shallows on the other side of the chain. One small island has nothing but little iguanas.
There is also a wreck or two to dive.
I think in the three weeks you could then head up to Bimini and get some sharks and dolphins. The keys on the way to Bimini have some good diving. I think the problem will be knowing where to dive as most people keep diving spots to themselves. It is there business so hard to blame them.
I think the Bimini/Exuma area is not hard to find sites on your own though.
You could always follow the Blackbeards boats to see where they dive and plop in after them. They have 3 sail boats and are not hard to spot. They are in the Bimini area and have a Cat and large liveaboard in the Exumas.