In the past I have used disinfectant bleach wipes and they work a treat. I guess the U.S. equivalent would be Clorox or similar.
You will probably use quite a few and you'll need to do it at a time that you're not going to fly straight after to allow the cork to dry.
Be careful not to get the bleach on any painted areas too.
Hope this helps!
Ps, test a small area first to be on the safe side.
