Currently the QR code inserted in a delivery (through the module custom link inserted in the delivery body) is generated as an image file link, thanks to the server-side barcode.jsp script. And the parameters for the custom link setting how the image must be generated are the type of barcorde (QR, EAN128, etc), the size, resolution. The color is not a factory parameter.
So the only solution could be to adapt the barcode.jsp file located on server-side. You can read the Java Server page code, it is pretty understandable. But I recommend to duplicate the barcode.jsp and modify the duplicated file, in order to keep safe / maintenance by Adobe for out of the box module. If you are On Premise hosting, you can achieve this change by your own.
Alternative: ask Adobe for an evolution of the barcode module, with additional parameters.