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 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. 
 yeah, i most certainly don't want nickel metal in contact with my skin, even if only just my hair, what an awful choice of material... chrome is more neutral to sweat

really what you'd want is it has little springy pins on one side that actually anchor the induced current to your skin

the main point of all this really would be, if it had a point, soaking up the frequencies and mushing it together in a small, safe DC current

overall, earthing is probably more effective, just a copper plug in your shoes that earths you, then your skin acts as a shield, conducting the radiation electrons quickly into current and getting it away from you 
 also, just on the last point, it's not about neuroelectric signal induction, although that may at some point matter, but probably not without an implant into your brain - it's about the moderate ionising effects of especially microwave bands like 20 and 80ghz, and more generally, the clouding of sensing of schumann resonance diurnal oscillation timing and its effect on endocrine clocks 
 Cave man not know what you talk about. Cave man just walk on grass. 
 cave man get drownd