Figure 1 is my implementation.Figure 2 is the effect I want to achieve.
Model it in Blender? That seems like the easiest way, especially if you have a specific shape in mind.
Then you can either texture it in Blender and load it into three.js.
Or you can just save the geometry (with UVs mapped) and load the geometry in three.js and, at the same time, add the texture in three.js.
I used to create islands in Blender and use a transparent texture to provide a detailed coastline.