Radium in watch dials?

As someone that sells watches on eBay, I've come into contact with several peculiar people, the latest of which all of a sudden didn't want a watch he just purchased because the dials are coated with radium to make them glow. Now, as far as I know, the use of radium as a source for luminescence on watch indexes was discontinued in the 60's not because of health risks for the wearer, but for the person assembling the watches, and thus coming in contact with the radium much more often.



Is there any rational reason to be worried about it?