I had an old radium Omega that I sold recently. I've also got a few vintage pieces that are almost certainly radium.
I was also a bit worried like you but after some research concluded they're fine to wear.
The radiation given off is alpha radiation which will be stopped by the glass and can't penetrate the skin anyway. The only slight danger with radium is ingesting it so don't eat any of your dials.
In fact I wrote this blog post a while back:
When the first wristwatches were being made for WW1 and WW2, it was decided that glow in the dark dials would be very useful, for obvious reasons. The new wonder substance at the time was a radioactive element called radium, as discovered by the Curies in 1898. Given the huge lack of knowledge of the effects of radiation at the time, radium was used for everything from pepping up soft drinks to bathing in for therapeutic effects.
So, by combining glue with radium, a man called William Hammer created undark, a glow in the dark paint. Hundreds of young women were hired to paint aircraft dials and watches. They used to point their paintbrush by licking it, and some even painted their teeth and fingernails for fun. This meant they ingested a huge amount of radium. Radium is a bone seeker which once ingested attached to bone material and destroys it. Suddenly, many of the women became very ill, often with jaw problems and many died from it. You can read more about this tragedy http://www.damninteresting.com/?p=660.
There are still hundreds of thousands of radium watches out there, all still highly radioactive. The risk from wearing a radium watch is miniscule but they should be treated very carefully when opened and only professionals should try and repair / remove the paint. The danger is really only from ingesting the paint rather than the small amount of radiation that will get through the glass.