I believe the tin foil hat is suppose to be reflective - much like a radar reflector.
The round design is probably not the best option. For radio wave reflection you want flat surfaces. The traditional folded paper hat style would be much better:
Remember, you are mostly concerned with RF radiation coming from orbit so you need to construct your hat to protect from above. I would think a graduation cap type design would also work well.
If you want to test your design, try placing a commercial radar detector under your hat, then ask your local LEO to fire his radar gun at it from overhead.
To be perfectly safe, I tin foil hat may not be enough. You may want to look at building a Faraday cage. You can even make a simple, portable Faraday cage out of aluminum window screen. Think of a phone booth sized box made of PVC pipe or 1x2 slats wrapped in window screen. You can pick it up and move around with it. Make sure to give it a 'tail' of light chain or aircraft cable so it remains grounded when you have to lift it off the ground to move.
I hope this helps.