A really good logo animation tells some kind of story and has a hero. The hero is usually the company name or primary component of the logo.
If you want to use the hammerhead shark and make it look more natural you are going to have to use some traditional cell animation techniques. Just using puppet pin on the layer is not going to cut it very well.
Maybe something like having the shark swim from behind the camera and then circle the logo once before it pops into position. This may require a few drawings. You also have to use basic animation techniques such as anticipation, elasticity and exaggeration. I would probably also be moving the logo up and into position. The entire move would take maybe 30 or 40 frames maximum, then I would hold on the logo and add some kind of moving overlay.
My intitial thought after seeing how the puppet tool worked out is that tradition animation is needed to make it look natural, either drawn frame by frame or a rigged 3d model that's animated then rendered to look like a 2D illustration. Or stock video of a swimming shark with a moment where the position of the shark is close to what you need. Then manipulate the "visual look" of the video to fit & at the moment where the shark is close to the position you need fade it to the drawing. Or: The puppet tool might work better if yoi had a second illustration of the shark that was not in such a dynamic pose. Just a straight (like a T-Pose) shark that will deform less when bent either way, then have it switch to the final drawing. If you got money there's a plug-in called Newton that's interesting. Among other things, You can pull shapes around with it and have the "tail" follow in an organic way. But I'm not sure if it would work on a larger illustration that wasn't just a straight line.