Then that's what you should change, since there's no good reason to maintain any of that on your computer or another device you might use for any reason I can think of.
The only information you need when calling to report a lost or stolen card is your personal information and any security information they use to identify you, along with the customer service phone number for the card company.
Otherwise, none of this information is ever needed except when actually using the card itself. And if the card is lost or stolen, it should always be immediately reported and disabled by the card company.
So again, I can think of no valid reason to ever duplicate any of this information, since all this does is add risk that this might be stolen by someone, either via the computer or simply someone who has access to your house reading it off the paper.
Rob