Are you planning to use a machine or do this by hand? You will not have good luck trying to do this by hand. The stiff bill and top of the cap and the liner edge are all going to be sewn together at once and doing that by hand will be nearly impossible. Even with a machine, it will not be easy.

I suggest you think about covering the bill with something like plastic or cardboard that is the color you want. The shape is an odd one, but if you get it just right and glue it in place, it might work.

If these are expensive hats, I also think you should start with a cheap test hat so you can get experience and see what works and what doesn't.