I've had a thought about the manufacturing of evidence. What if, after finding the fin, she finds whatever the fin was made of? Something odd or imported, that wouldn't be common on the island, and would limit the 'suspects'?
Logs, chains, anchors and tar would be common in a fishing village. Unless something other than an anchor is used as, well, an anchor? A distinctive piece of stone, or a lead or iron something-or-other. The murderer is the town clerk, I've no idea what he'd think of. What is the fin made of? A piece of wood is hard to identify, a thick piece of leather or parchment (covered in tar for stiffening, as well as protection). A piece of copper or brass that's been cut from something else?
What does the clerk's no-good son do that would give his father access to things-other-than-paper?
Actually, leather or rawhide wouldn't be bad, if it was disposed of in the sea fairly recently, it might be of interest to the shark. In fact, maybe the murderer just shoved it under some other stuff and ignored it, until your MC shows up. Then he thinks, "Uh-oh, better hide the evidence," not realizing that she isn't going to be doing a house-to-house search.
So, he dumps it in the ocean, because in a sea-side village, that's what you do. (Possibly weighted with the same sort of chain that he originally used. Check out the variety of chain links available.) It's a thick piece of leather left over from some long-ago town job, that the clerk has inventoried a dozen times, but figures everyone has forgotten, come fin-making day.
So there's the chain and a side of hide with a fin-shaped piece out of it. Useful evidence?