Thank you for reaching out and posting this question.
There isn't a way to change the credit card on an existing order without recreating the order and processing the credit card again. In order to do that, you would need to refund the order and the customer can place their order again using the other credit card. While you can copy the tracking from the original fulfillment and use it as the fulfillment for the new order, it's also important to note that the credit card processing fee may not get returned to you from the refunded order depending on the payment gateway that you're using and the location of your store. For this reason, it may not be worth the trouble to re-process the order in this instance.
That being said, I noticed that you're a new member of our Shopify Community and I'd love to hear more about your business. What types of products are you selling? Do you have a marketing plan prepared for your store?
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