I don't see how you can do anything other than print it on white vinyl....Siser for example and then contour cut it with a 1mm edge all round. At least that way you get the white and the whole thing will stand out nicely against the navy colour of the polo.
Is all the white in the image the colour of the Polo or is the "Swoosh" white too? Exception being the star. If the background is the polo then cut it and tell the customer that the detail in the star is too much and that you have to reduce the detail a little so you can cut and weed it. It wont look bad.
If its all white then use the BN20.