In my opinion, the concept of a "hat" is outdated, because the radiation has a wave nature, and the hat only shields the upper part of the head. Therefore, a "double-cap" is needed, which would completely isolate the head from above and below, and to the sides from any radiation. And at the same time - from the body. Foil bun.
From my experience in shielding electric guitars, I can confidently say that a cap without grounding is useless. So be sure to have a grounding wire.
It should be protected from magnetic interference with a double permalloy, but this is no longer a hat, but a helmet.