I recommend not bothering. Liability for fraudulent CC activity (in the US) is very low (max $500), and banks never enforce the liability for two reasons: 1) it's easier for them to chargeback the transaction to the vendor, thus they're not out of pocket, and 2) it causes customers to leave for a provider that doesn't hold them liable.

How much of your time spent chasing down and changing a CC number is worth a maximal risk of $500 with a vero low probability of occurring?

EDIT: Thanks to nenolod for the correction!

Since Dodd-Frank, debit cards and credit cards have the same liability protections.

> maximal risk of $500

I'm pretty sure you're off by a factor of ten. If someone makes fraudulent charges with your credit card, your maximum liability is $50, and you'll only have to pay that if the charges occur after you've reported the card stolen. (There are different rules for debit cards, that doesn't apply here.)