Cosmic rays aren't electromagnetic radiation. They are instead extremely high-energy particles that travel through space at very nearly the speed of light. Completely different physics.

OK...I don't want to get into the weeds here, but that isn't entirely correct. At our project we had to parse Cerenkov airshowers into photonic and hadronic. Both are "cosmic rays" (though we don't generally call them that...we call them alphas, or gammas, or whatever they are). Our specific goal was weeding out the hadronic showers and analyzing the photonic (gamma ray) showers.

Gamma rays can be excruciatingly energetic, and will rearrange your DNA (and other biology) pretty effectively. Our energy regime was about 500 MeV to about 4 TeV. There are detectors that go even higher.

(Hadronic showers are the result of hadrons striking the upper atmosphere, hadrons being anything comprised of quarks, which include protons, neutrons, alpha particles -ionized helium-, and the like.)

I would not want to be struck by any "cosmic rays", photonic or hadronic. Over time it will kill you.