A detector that picks up Alpha can get pretty darn expensive. I can pick up Beta and gamma. What I’m actually reading is the radon gas emitted from the radium. no harm once the watches assembled. And as long as general precautions are taken, no harm working on them.Fortunately there is not enough radium in the hands to emit a significant amount of radiation (a gram of pure radium or more though becomes concern.) You are smart though in ventilation and PPE is wise since inhalation of the dust is a potential hazard, even in microscopic quantities. I have some old radium dialed aircraft oxygen gauges, a pocket watch and a couple wrist watches, it's amazing how hot these things are when you count alpha, beta and gamma radiation. I like viewing them in the dark with a 10X loupe, you can see the scintillations in many instances if the paint has lost it's glow.
Trust me, I’m not painting dials and licking the paintbrush like the radium girls! A lot of misinformation out there about radium watches. A couple really good videos out there citing government studies on their effects, and how to work on them properly.