I see that it's pretty laggy with WaveyCapes. :/

Depends. What was around you when you did this? If there was a lot of players around or a lot of nothing around(empty flatworld) this is probably expected.

Trying on a normal multiplayer world the simulation takes 0.08% of the client time.

Depends. What was around you when you did this? If there was a lot of players around or a lot of nothing around(empty flatworld) this is probably expected.

Of course with a lot of players, how do you expect to check the performance of something that's not on the screen? It takes 200-300 fps from what I checked.

Still not sure what you want then^^? This is the expected behavior.
I mean 20% of the client tick is updating the cape simulations (other than updating positions and angles nothing else happens there) and 3.8%? of the render time is used for the capes. Don't see anything that needs optimizing here? (You also have to remember that the cape has more geometry than a normal player)

It takes 200-300 fps from what I checked.

If 5% = 200-300 fps, then you have 4000-6000 fps, I doubt that. In your extreme case scenario of probably some game lobby like Hypixel, it made the game 5% slower for the eye candy.