An important question is HOW radioactive is this water?
Barely enough to be TECHNICALLY considered a hazard, or is it REALLY radioactive?
If you immersed yourself in it, how many millirads per hour would you get? Got to get up to a pretty decent stack of millirads to really be dangerous.
Details matter. Lots of things are radioactive, like the ash in your fireplace.... just not radioactive enough to be an actual hazard.