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!