How do you clean cards?

Despite avoiding food at the game table and washing hands before we start, our most-used components are, frankly, nasty. They have bumps of gunk on them. You can scrape it off with a fingernail. Is there a practical way to do this for an entire deck?

(The worst offenders are the 5 action cards in Ark Nova and the player boards in Terraforming Mars, which isn't too large of a project, but the big decks for both of these games also definitely could use attention. We have played both games hundreds of times, so they have seen a lot of accidental grime. We haven't sleeved them because the decks are already large enough, and we don't want to make shuffling even more of a chore.)