Alpha (two protons and two neutrons) is the largest form of radiation and is harmless.

Beta (free electrons) isn't much stronger, but can be if ingested in large quantities. Doesn't pass through your skin, though.

Gamma (this is probably what you're thinking of, the ray type of radiation that has no mass) does pass through your skin, and too much can certainly cause health issues.

And of course neutronic (those free neutrons that cause fissures) can pass through a lot of things and can certainly be lethal.

While beta isn't all that dangerous, you'd certainly want to get whatever is emitting it off your skin. And really, it's the same thing with any radiation. Something is emitting it, and if it's on your skin you want to get it off.