Put the purchase price on one of the name brand "gift cards" that work as a credit card (like "The WalMart Visa Gift Card"
https://www.walmartgift.com/wmgift). You can get them in the store (make sure that they put the full amount needed on the card and you pay any fees seperatly) so you can pay by cash, check, a credit or debit card, or whatever the store that sells it normally takes.
This "gift card" will only hold the amount you desire so you can use it as you like and any loss it totally limited to that amount. Once you've got what you ordered and no longer need the card, simply toss it (or shread it would be better) and you're safe from the on-line hackers. Please note that there are two types of these cards, one-time (you put a set amount on the card and once that's gone the card's canceled automatically) or reloadable (you can go back to the store with the card and put more on it later if you wish). The one-time cards cost less and are safer, but either way the card isn't connected to your other accounts or credit.
If you make your purchase using that card and someone later hacks the on-line store you purchased it from and attempts to use that number, the balance is zero (unless you reloaded it for some reason) and they get nothing. Since the card's canceled, they even risk getting caught since they're attempting to use a canceled credit card (but that's generally easy to talk your way out of - e.g. "I guess my wife gave me the old card"). Your only risk is if they get the number and attempt to use it prior to your order's charge going through. This risk is minimal (unless they steal the card or something like that) since nearly everyone uses a real-time connection for their credit card transactions.
While it does cost a bit more, it allows you to safely use a credit card on-line that isn't tied to you or your credit line. The down side is often regular credit cards provide some type of consumer protection ("I ordered this but they never shipped it to me so investigate and remove the charge from my card") but these generally don't have the same kind of protection (especially the one-time use cards where adding any amount to the card is locked out).
Please note that since most on-line retailers validate the user's name & address matches what's on the credit card, you'll need to register your gift card as the instructions state to place it into your own name or this validation will not work. From the WalMart site linked above is this notice:
Please Register Your Card To:
• Shop online, by phone or mail
• View past transactions
To shop online or by phone, you must register your Card. Merchants need to verify the billing address associated with this Card before authorizing your online or phone purchase.