I don't think it would be a problem. Just negotiate the rate before hand depending on how many of you there are it shouldn't be too expensive. My guess with the people we ride with would be between $5-10 per person. Some may think that is high but we are always happy to pay and know these people are just trying to make a living.
West Bay to AKR is not a normal route but as Funnie says, the local are hungry, arranging it should not be a worry with enough notice.
We stayed at Sandy Bay and swan to the reef each day. We always had to watch for the boats going to and from Anthony's Key. I can only assume these were not all organized package tours?
AKR is one of the original dive til you drop all inclusives. Depending on the size of the boats you were dodging, my guess they were part fleet of dive boats.
I expose iris possible AKR would b3 willing to send a boat for the OP.
These were a smaller type taxi boat holding a few people, one or two even, and not the dive boats, which usually go out to the right.
Hmmm, wonder what that was about....perhaps the water taxi have changed their MO.
Dive boats at Anthony's Key Resort have the name on the side of the boats. They've got a BIG fleet (11 dive boats+ 1 snorkel boat) -- and each boat is clearly advertised!
Maybe the little boats were local fishermen? Or just people with their own boats? There's a channel that cuts through AKR and makes for a much smoother ride than going out along the outer reef. There are docks for the homes out "that way," too. Lawson's Rock is further up the coast. The boats may not have necessarily been going to AKR.
FWIW, we've gone on water taxi type boats for private half day snorkel trips from WBB up toward Palmetto Bay, stopping at the dolphin encounter if there was a show. So agree with others that shouldn't be a problem for you to negotiate a boat ride.
What day is the dolphin show at AKR?
Some of the smaller boats are the ones that run guests from the Main Island out to the Key, I am sure, as others have mentioned you could find someone to take you to AKR, but there could be some issues, (1) Who is allowed to pull up to the AKR Dock and (2) difficulty getting a small bot fror the trip back unless you pre arrange something ot pay the captain to wait