Ive used pre-paid cards for online purchases for years for that very reason. I usually
buy a Vanilla Visa gift card because the money is available within 30 minutes and you can get them at drug stores.
You can also register your email and zip code on the vanilla visa gift card site. When it comes time for check-out click the credit card option and enter the your info like this:
First Name: A Gift
Last Name: For You
then enter your mailing address and make sure you update the shipping information with your real name and address. I mustve ordered 50 times from dozens of different online vendors and had zero problems doing it like that.
If for some reason that doesnt work on their site, you can always call them and explain that its a gift card and see if they can take the info over the phone.