The beta emission is trivial and harmless. Alpha particles travel 7cm in air, glass absolutely stops it. A sheet of paper would.
Its perfectly safe to wear.
The paint on the watch hands contains radium and decay products but in tiny amounts. If the crystal broke wipe cup the dust with damp paper towel. Itsjust not that big a deal.
Itvwss most dangerous to the people whomade them, exposed daily during a career. Andcl the placecthst had gallons of thecshit laying around.