Then you cannot shop online. You must be envisioning some kind of fantasy world where CC transactions never have to be examined manually by human beans. Sorry, you can use PayPal or whatever you like, but there's always a certain percentage of transactions that end up involving a human. That percentage is never zero. I guarantee you that the PayPal employees involved in that task are doing it electronically.
Ah, you prefer to shop at sites that lie rather than those that tell the truth. There are many available for your shopping pleasure.
If you're going to do your own CC transactions (e.g., get a merchant account, as thousands of small businesses do), then you're going to store card info electronically. How do you figure merchants handle chargebacks, refunds, reconciliation, etc. -- scribble card numbers on post-its that they stick on the wall for 90 days?
People are superstitious about what they don't understand. Thus, we have people worried about their CC information residing in some merchant's browser cache, but not the least bit worried when they hand their credit card to a minimum-wage waiter who looks like a meth addict (or better yet, shows their debit card number to the teenage cashier and then punches in their PIN in plain site of same).
If you shop online regularly with a credit card, then your CC number is already residing on hard disks around the nation -- often completely unencrypted. Just bothering to encrypt the info before it makes it to disk will put this developer ahead of many of the folks you do business with. (As usual Amazon is at the top of the game here, at least if you believe their claim of piping the CC info into a secure machine that uses a custom protocol and does independent checks for suspicious requests. But of course, they still have to store CC info on disk, and they still have to be able to manually inspect it when things go wrong.)