ZigzagPX4
The Swiftness of the Ranger
If Shaun is dying of cancer wouldn't that also imply that his DNA was never viable in the first place? I mean he has never left the Institute in his entire life so his cancer didn't come from radiation exposure (or maybe it did from the bomb at the beginning and the Robotic nanny with the atomic battery) so he probably had a pre-existing genetic condition too, maybe your character does too.
I think it was just supposed to be Bethesda's mishandled attempt at irony. The "special one", never exposed to radiation and the leader of an organisation that prides itself on being the most pure, got cancer. Meanwhile, the rest of the wasteland is exposed to radiation daily and never gets cancer.
But seriously, I agree. Cancer by genetics is pretty common, and if we are to assume that the Fallout universe doesn't have cancer...
(Which would explain A LOT, including how the nonexistent risk would explain the focus on atomic energy since research and experimentation would not put off people if it presents no fear of cancer, and as a result of subsequent events the world switches its entire focus no longer leashed by the fear of radiation. Change in scientific culture would influence the general public, causing slight differences in political decisions, and the divergence in the timeline occurs. But that's just a theory, since there seems to be a subtle shade of "cancer exists" in the lore I may have missed.)
...then it would be one of the few possible only ways to actually get cancer. But I suppose we'll never know the truth, thanks to Radiant™ vagueness.