The advantages to laminating a flattened-out cotton ball to a wallet card are:

1. I'd normally be carrying the wallet card anyway, so why not?
2. It's waterproof.
3. You really don't notice it's there, any more than you would notice a credit card or library card.

The disadvantage, of course, is that you need a knife or something sharp (or strong teeth) to rip the plastic laminate open.