I was thinking the same. However, the problem is not to avoid people from getting in and causing harm to themselves, but them getting the dangerous stuff out and causing harm to others who actually heeded the warnings. You'd need extremely strong radiation

If you're talking about 10,000 years in the future it may not matter so much since the radioactivity would be much less after so many half lives.

Exactly. You can't rely on the radiation itself as a deterrent.