The thing about genes is that if there aren't natural selection pressures to keep certain traits, they tend to drift, and traits can change or become entirely non-functional over a surprisingly short time. I would expect, unless there was a concerted effort to maintain the radiation detection trait over those 10,000 years through careful breeding, the cats would lose their radiation triggered appearance change behavior before it actually had a chance to be useful to people.
In 2004, a Danish company created mine-detecting plants that changed color when their roots were exposed to landmine leakage. So yeah, this actually makes sense that we'd imagine this kind of solution.