polaroid flash

[leeb5]

hi all can anyboby help
I have a miniportrait photo studio polaroid camera that takes 4 identical pics for passport photos, it has the flash on top. the problem is when i take pictures if the subject hasnt got long hair you can see a dark shadow cast onto the white background just below the ears, i suppose its from the flash on top of camera. I have to use the flash to get the light can any boby tell me some relatively easy way to either eliminate or reduce the shadows. Would a off camera flash,lower than the camera pointing up connected to the x syn on the camera help solve the problem ?
any help apprieciated