Unfortunately Privacy.com requires the generated cards to be paid by a bank account (rather than a credit card). So you have to be okay with them having your banking info.
I got very interested in that service but it's ridiculously difficult to figure out how one's account get funded. I did find it at the very bottom of [0]. Also restricted to US customers only. They're not that much better when it comes to dark patterns if the "How it works" section completely neglects the part where and how you pay THEM.