This article on the Horological Meandering discussion forum is excellent -- Watches and Radiation Risk. You might want to read the posting if you own old watches with radium dials and hands (and even bezels).

Here are the author's recommendations:

I think there are clear and identifiable risks associated with wearing a vintage watch with Radium-226. Those risks vary, but in certain circumstances are very high. Collectors should appreciate that a Radium-226 dial poses a real health risk not only to the wearer but also to those in regular close proximity to the wearer. That risk will vary depending on a number of factors and I would put forward the following checklist;
• A simple Geiger counter can be purchased at a reasonably low price. This will enable a quick test to evaluate how much Gamma radiation is evident in a watch. Generally speaking, watches with radioactive lume manufactured between the 1920s and the 1960s will, typically, have had Radium-226 applied. That is a decent working assumption. Some will have different isotopes with much shorter half-lives. For Radium-226, however, expect the Geiger counter to light up.
• If a watch is identified with Gamma radiation, evaluate at what point you feel comfortable with the risks. Clearly, a watch that emits over 10 uSv per hour is one that I would simply not want to wear. It would be the equivalent of having 1-2 chest X-rays every single day. One that emitted at 1 uSv per hour might be something I would wear intermittently. Everyone will have their respective tolerance levels. uSv 100/hour? I actually wouldn't want to be next to someone with such a watch.
• With Radium-226, be aware that it carries a much greater risk to health if the watch is worn overnight courtesy of the Radon gas emission as well as the higher vulnerability of the head to Gamma.
• Radiation dust that will exist on the dial is toxic. Never open a watch. I think this rule needs to be quite categorical.
• Radon testing kits are very cheap and easy to use. For collectors that have Radium-226 watches, especially those with large collections concentrated in the same place, it would be a great idea to test for Radon.

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: Just spotted this on Instagram, from our old friend Peter
: Charlie -- https://www.instagram.com/p/BB0Hd08m9KK/

: Jeff

: A video posted by PB (@peter_charlie) on Feb 15, 2016
: at 8:53am PST
: