I use square for my tech support business, it works as a good platform / example of how the transaction process might be able to work with a bitcoin wallet app. Either it does not require that you have the card, you can manually key in the CC info as well. Square has no idea what was bought, your CC company won't see the transactions as bitcoin.

But then who is going to email their CC info? I would hope very few unless they were using onetime use cards.