You need to change your shipping options to "Digital delivery". For digital delivery, all you have to do is message the 10$ Amazon code, located on the back of the gift card, to the winner in a message. Hope that helps. :)
You type the numbers on the back of the card in a message to the winner. You don't need to mail it. I will bid but would want the code. That way you will get your credits ASAP also!