Hi Gray Wolf. The 2 options we were offered were (i) Sail across to the volcano island, walk around near the water for a short while, then sail back again; and (ii) Sail across to the volcano island, trek up the volcano to the rim and then return. The second option was not fully available due to the volcanic activity alert level at that time, so we decided just to take the boat trip and maybe take the second tour sometime in the future.
We were not offered an option to circle the lake, but I am sure you could negotiate a price for that if you wanted.
Richard