As long as your hair is dark and your skin is pale, you will have a shadow, even with a close shave. If you just recently shaved, it will get better as your freshly shaved skin gains some color - some guys speed up the process with a self tanner lotion. However, I do not advise spending time out in the sun without a good sunscreen - the fresh shaved skin will burn quickly.
My hair has essentially all turned white/gray, so my shadow does not show. So you could hope that you turn gray soon.