Only if the wild animal is playing Fate with you.
(Please don't play RPGs with wild animals.)
Concession, as a mechanic, specifically faces outward to the real people playing. It's explicitly about the parsing of narrative authority over the fate of the character post-conflict, and nothing else.
Characters do not concede. People do.
So it's basically like this:
The consequence of getting taken out is that the chief advocate for that character (GM included) gets no say over the fate of that character after that scene. Theoretically, anyone who takes anyone out in a physical conflict could follow that up with, "...and I kill you," and barring social contract disruptions in the group, that assertion stands.
If you concede before you get taken out, you as the chief advocate have the final word over the fate of the character after that scene. The bit that's up for negotiation is how we express the terms of your defeat in the fiction, but the chief advocate gets the last word.
-- Fate SRD, "Conceding the Conflict"
When you concede, you don't concede to a savage shark or a howling tornado or Perducci with a harpoon gun, you concede to the GM. A concession is something that's worked out between players; the characters can be set aside for the moment. Character desires don't necessarily have to matter unless they were important to the table narrative, and unless you've dropped into a situation analogous to, like, Maneater or some of the Jaws sequels, the shark's less a narrative agent and more a force of nature.
But this also makes things a little more difficult. If there were some party in the conflict that wanted something more than to be destructive, you'd be freer to work out the compromise as giving them what they want with minimal opposition on your part. Perducci isn't in the scene to skewer you with the harpoon gun, he's in the scene to make a getaway with the serum, which he can get easily enough by knocking you out and tying you up in your own ship's hold while he sails away. When dealing with destructive forces, like a howling tornado, or a raging wildfire, or a shark that just wants to chomps until it can't chomps no mores, you've got a couple of things to consider:
- is dealing with them actually a conflict? Could you be capable of significantly hurting them to force a concession? Fate Condensed makes it explicit, but a lot of versions of Fate have the option of running a hybrid con(flict|test), where some of the participants are trying to stress others out, while the rest are just trying to rack up contest successes to e.g. get back on the ship or to a fire shelter.
- what's actually a compromise in this case? If you're trying to outrun a wildfire but wind up having to concede, what happens as a result? It's obviously not in the cards that the wildfire burns you to a crisp and you die, because conceding gives you control over your own fate and if you could only hope to die you might as well go out fighting, right? But it also doesn't feel right that nothing further happens - that's what you were trying to get out of this scenario by getting to the fire shelter, but you gave up.
The obvious way out is to take some consequences, but that's gone in this case, since there aren't any chomps left on your character sheet. Here are some ideas for playing it out that might be fruitful, since they do still have to connect to the rest of the plot you've got out there.
Wait, have you got chomps left on your character sheet? You may have the option of taking an extreme consequence depending on which Fate version you're playing with, rewriting one of your aspects to reflect this dramatic travail (and only clearing it out with something less horrific when you hit a major milestone and rewrite an aspect). But maybe that option's not available, or maybe your chompee would rather not end up, for example, Mauled Beyond Recognition.
The shark breaks something (personal). This does depend on the ongoing story, but it's likely that the shark can break something to serve as a plot obstacle beyond just one character dropping out of the conflict.
It shears off your scuba tank regulator and swims away in a panicked cloud of bubbles.
Or, maybe, crushes some electronic gear and swims away after a stinging shock. Even if you've just assembled your gear by convention, in order to continue on now there's going to be a challenge to repair or get by without it.
The shark breaks something (less personal). If everyone's cool with it the shark can break something entrusted to the group as a whole rather than something carried just by the character doing the conceding. Like the ship that got you out to the high seas in the first place?
You frantically swim back and pull yourself to safety, but the shark just keeps after you, thrashing and thrashing until it's torn a hole in the hull and the ship starts to take on water.
Oh, I'm saved! ...oh no, I'm saved!
You drift away from the shark and then abruptly you're swept up in the wake of an escape sub! ...Perducci's escape sub. And in your condition you're pretty much just a hostage.
Even if there isn't necessarily somebody set up in the scene to want something, it might be possible to introduce somebody in the scene to want something less destructive to your person as part of the concession process - in this case, Perducci's people would really like to abscond with your unresisting chomped-on self.