Best way to animate a top-down 2D fish?

Hello, recently I've been trying to create a controllable fish character. The game is 2D and top-down.

My two approaches are:

1. Rigged Animation, which is versitile but looks too robotic. For example, no matter how hard I turn, the fish has the same turning animation.

2. Procedural Animation, which I implemented using s line renderer following a tutorial from the channel Blackthornprod. It is very close to what I want, the fish is dynamic. The problem is that the fish loses all form when turning, some parts get thinner while some parts get thicker. The other thing is that it's hard to make it work with different types of fish sprites.

I want to be able to keep the structure of the fish, but still move it around in a way thats fluid and smooth. Preferably avoiding line renderer as I'm not too comfortable with the pixelated edges and needing to loop through hundreds of positions to anime only one fish.

I would love any suggestion and I'm thankful to anyone who takes time to help me!