Dennis, you would need to study the ORN volumes to see which vessel/s was/were in the area at the time. However, because it was customary to have several ships on blockading duties at a time, it may require that you search the deck logs of more than one vessel, and this could be quite expensive, unless you are able to do it yourself, at the National Archives.
I will check to see, in my volumes of the ORN, if I can find out which vessel or vessels were in the area at the time.
Do you have any idea in which exact spot of North Florida he was taken prisoner, please?
Some of the blockading squadrons did include summaries of the vessels in their squadrons, and where exactly they were stationed at certain periods, and these are shown in the ORN volumes.