You need the mallet, and the old man has to be in the right place to catch the fish.
To get the mallet, stand on the floating statue. The other end will pop up with the gong. Push the old man to the right, to near the barrels on the right side. Use the mallet, and the fish will jump to his line. The map piece is in its mouth.
The shipbuilders are on Dragon Cove.
dragon cove by far
top left is dragon cove
You buy the ships on Dragon Cove Island with the Chinese people.
go to the dragon cove and go all the way to the right
Dragon Cove. To get the mallet stand on it's head.
Keep trading in a clockwise path until you have 3000 doubloons. Then go to Dragon Cove and buy a Jimmy Rigger.
in dragon cove
dragon cove
Buy boats with doubloons
The shipbuilder (Ship Shape Shipbuilders) is just to the right of the Trading Post.
When you have enough doubloons, from salvage or trade, you can buy a larger ship at the Shipbuilder on Dragon Cove.