In my opinion, the effect of radioactivity is not very thrilling, because it's just another poisonous gas (except that you can't see it this time). Also, the damage it deals instantly on your character is rather high and not that realistic, radioactivity does not work that way.
I think it would be really exciting if it was like deadly and cruel, but in a more long-term way. As an example I would say:
Instead of just dealing damage (depending on the distance to the U-ore) in a certain area around the uranium, just increase a "exposure" (let me call it E) variable (depending on the distance to U-ore). Then add the value of E to a "cummulative exposure" (CE) after an initial offset-time has passed (which could be strongly dependent on E) and just deal the player randomly damage (depending on CE) with a certain rate (also depending on CE).
Tricky part is when to reset CE to 0. Just after the first death? Then you could just jump to death and grab the lootbox later. Better something like the first death after 2 hours of no exposure. That would be really cruel.
That whole thing would cause in a gameplay style that is like: "Hey, there's a snail here, you can grab it easily, but it will damage you continuously for the next 2 hours or so, no matter where you are."
I really think this would make the whole radioactivity thing more exciting.