Swimming to the bottom, touching your elbows to a fresh fuel canister, and immediately swimming back up would probably be enough to kill you.

Yet outside the outer boundary, you could swim around as long as you wanted—the dose from the core would be less than the normal background dose you get walking around. In fact, as long as you were underwater, you would be shielded from most of that normal background dose. You may actually receive a lower dose of radiation treading water in a spent fuel pool than walking around on the street.

xkcd What If? #29

So you’re saying that you can swim in an energy drink?

New set of gender goals: Radium Girl.