Are cotton based cage accessories safe?

I'm considering buying my IRN one of those spiraling cotton accessories
that hang from the top of the cage, are they safe to leave in the cage
when the bird is unsupervised?

I know rope accessories can be dangerous if they are eaten by birds, does
this apply to cotton based products too?

I like to avoid buying him things that require supervision unless he's using
it when I have him outside his cage and he has my full attention.