The Radium Girls ingested the Radium by licking the points on their lume application brushes, totally unrelated to wearing a Radium dialed watch.
Here's the bottom line...
Radium is comprised of a number of isotopes - including 223, 224 & 226 - all of which are present, in various quantities, in any 'lump' of the substance. These isotopes are hazardous, but only at very short distances. They do emit highly energetic charged particles (Alpha & Beta), but these particles do not travel very far at all... they will not penetrate the skin from an external source, for example.
So wearing a radium lumed watch is no problem whatsoever - the 'dangerous' particles (aka 'radiation') will not make it through the glass or metal of the watch, let alone into your skin.