**** that! I reckon cleaning will take too long, plus you will possibly have to do it each year when you receive your new licence if you have any renewals of ratings like IR etc.
I am told that the plasticiser in the ink on the pages reacts with the plastic wallet.
First buy a new clean licence holder.
Put a piece of tracing paper between each new page of your licence and the plastic pocket. I cut a piece big enough to fold in half (A5?) and put each page between it.
No more sticky licence pages and you can still read everything on your licence through the tracing paper, albiet slightly "softend" in its appearance.
Cheers!
Z.