Hmm, so either you get a mutation/new growth that's not "just cancer" or you simply take damage that heals over time.
I like the idea of measuring dosage in Grays simply because it's a really, really ominous name. "You have two Grays." 5 grays of acute exposure gives a 50% chance of dying within 14 days. I could use that to scale a Con save DC and the amount of hit point loss.
I like the idea of the group finding a "magic amulet" that makes clicking sounds that go up in frequency as they enter more dangerous areas, but I feel like most players would immediately figure out what's going on... and it's pretty hard to not metagame radiation exposure.