Radium can be dangerous, but more for the watchmaker than for the person wearing the watch. I am very careful when working on a watch that still has radium paint on the hands or dial. For the most part, the movement and case will block the radiation, and the crystal will also, so generally speaking they are safe to wear.
Now to illustrate how the radium can damage things, here is a vintage Illinois pocket watch I serviced a while back - note the radium burns on the crystal at each number:
The owner thought it was on the dial, and sometimes hands can burn the dial if left in one spot for a very long time, but in this case you can clearly see it's the crystal:
Disassembled - replaced the mainspring:
All finished and with a new crystal:
Cheers, Al
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