Pretty much.

A few minor points:

- The gamma absorption of tin is highly frequency-dependent.

- You are a capacitor. Lipid layer of skin cells is a good dialectric. But you'd need to get rid of the cotton layer and have the metal in contact with your (preferrably sweaty) skin.

- Double-layer "supercaps" have too much ISR to deal with fast-rising potentials from radiation events. Tantalums are what you want there.

And, of course, unless you have electronic implants, this hat is mostly just a fashion statement. Sodium ion channel potentials in neurons are about 50 mV IIRC, you'd need a LOT of radiation to trigger that.