From my point of view the danger associated with the handling of watches with radium dials is heavily underestimated by laymen. Many watch makers refuse servicing or repairing these watches in our days because it requires a vacuum decontamination chamber to conduct such work safely. In order to protect your health and the health of your family never ever open the case of an old watch with an aged radium dial at home! Radioactive dust may already be evaporated if you just remove the cover from the movement.
Although the radioactivity of Tritium is less aggressive, Tritium ist no longer used by watch manufacturers for similar reasons. Who would like to be made liable for spreading health risks, if there is no technical justification for this anymore?
Heinrich