I was thinking of the wipe method BB but there are various methods that I looked at. I'm concerned that I don't mess up the info on the card if the more invasive methods are used.
I've wiped a couple of my cards with hand sanitiser gel two or three times each with no ill effects - the only thing I did was try to avoid getting too much gel near the metal contacts for the chip, I wasn't sure how liquid proof that area is and didn't want to risk it.
I wouldn't put the card in any kind of chip+pin, cardreader or ATM straight after cleaning it with anything wet (gel, wipes, etc) as dampness on the chip contacts could cause the electrical signals to go where they shouldn't. I'd hope the technology was designed to cope with a card that maybe had some rain splashes on it... but I wouldn't want to test that theory out with a card I was relying on using.
Otherwise I've gone with leaving the card for 72+ hours, flipping it over at some point to make sure both sides dry out fully. This is probably the safer option (for the card) if you aren't in a hurry.
Also, there could be an outside chance of alcohol in the gel dissolving the ink of your signature, but I can't remember the last time anyone checked my signature on a card so I didn't see that as a major problem if it happened (it didn't with mine).