First envelope the whole mesh to the main bones -- don't worry about the fins yet.
Next select the whole mesh, choose Envelope > Set Envelope again, and pick the fin bones. This adds the fin bones to the original envelope deformation. Make sure that Automatically Reassign Envelope When Adding Deformers is off or else the fin bones may affect the vertices of the main body.
So far the fin bones are part of the deformer list but nothing is weighted to them yet. Select the vertices of the fins, choose Envelope > Reassign Locally, and pick the fin bones. Now the vertices of the fins are assigned to fin bones and the rest of the mesh is still assigned to the main bones.
Grahame Fuller
Learning Content Developer