As I understand it (see: not at all), if you leave a spaceship with no suit on, you’d get baked like Marie Curie’s ovaries from the radiation. It’s mainly our atmosphere that protects us from most of the nastiest stuff. Would a giant cable reaching from Earth all the way to a platform outside the atmosphere become dangerously-radioactive over time? And if so, would that eventually cause the entire planet to get radioactive over hundreds of years? Kinda like if the hole in the Ozone layer were replaced with a Mario pipe.
And if that is the case, maybe we could forget the elevator aspect of it and just aim for a free eternal source of radioactive energy, like a really shitty Dyson sphere 👀
Any time you talk radiation, you need to be specific about what kind of particles, how much energy they have, and how much of it there is.
Most of the stuff in orbit is charged particles (electrons and small atoms) and low energy photons. Those get stopped by relatively thin layers of shielding, but if you’re not careful you’ll get cooked from raw heat.
Ionizing radiation like neutrons or x- and gamma-range photons can radioactivate materials, and take more shielding – think feet of water or a couple inches of lead. Nuclear reactors have that, but spaceships don’t. Fortunately unless you bring a reactor with you they’re rare enough that it’s not really necessary.
Substances become radioactive when they get hit by some kind of ionizing radiation and change into an isotope that itself emits radiation. Conducting radiation like a wick isn’t really a thing.
Electrons and small atoms are kinds of ionizing radiation when they’re flying around with enough energy. Also, it’s not the photonic type that makes something else radioactive (mostly). It’s the particles. Look up what neutrons are doing in nuclear reactors. They “contaminate” things that aren’t normally radioactive because neutrons ‘stick’ to their atoms and make the atom unstable because now it’s a different, most likely less stable isotope.