Credit card companies take care of losses from online fraud. You can get a paypal account (free) which is SECURE and basically acts as a buffer between your credit card and the retailer.
So you have
Credit card->Paypal
Paypal->Vendor
No one aside from you and paypal sees your credit card info. You can remove it at any time, and I can pretty much guarantee you no one at paypal will misuse your information. I have never heard of this EVER happening (and their infrastructure most likely makes it near-impossible to exploit from the inside). If there's ever a dispute, paypal will know how much money was sent, etc, so you will be able to get things resolved.
I work in information security. I'm a lot more paranoid than most, and I really don't feel comfortable hooking up my bank account to a paypal account. But I'm not too concerned with a credit card. There are lots of rules in place for electronic fraud, and it will be paypal or the bank who takes the loss the majority of the time. Not to mention, the only way you will ever get exploited is if you buy stuff from an untrusted site (which is pretty much your own fault) or if you give away your password (which again, is pretty much your fault).
I know you won't change your mind based on this, but nowadays it's pretty safe to go through paypal. I would say a lot safer than shopping in a store such as winners where your credit card info is SAVED and left in unsecure systems a la TJ maxx. Paypal at least knows how to secure data properly =P