Changing the Color of a Baseball Cap?

I bought a ball cap for my husband. He has been wanting one with the Chevrolet logo on it. I found one, but it is orange, red and white. I would really like to change the orange color to blue to match my drag racing truck. Is there a way to dye the fabric or paint only certain parts of an item?

I have never dyed or used fabric paint before. What is the easiest product to use for this type of project? I cannot submerge the cap as it has little LED lights on the peak, which is wired through the hat to a battery pack. I was going to just take a blue Sharpie to it, but wasn't sure how permanent it would be. I can see it now, it rains and the marker runs all down my husband's face, although that would actually be funny to see. I look forward to your answer. Thank you very much.

By She Drags from Ontario, Canada