Quick reply...

If the credit card includes PayWave, or something similar for contact-less payments... If your mobile phone includes NFC antennae... Then you may be able to develop mobile phone application which would pretend to be your-card-reader-plugged-into-phone, while in fact interacting with credit card through NFC.

Do you have some specifications, datasheet, or something, about what exactly your card reader is doing?

Thank you. Best wishes.
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Per aspera ad astra...