I recommend reading this article from the University of Northampton:
WWII Military watches ‘potentially pose serious cancer risk’.
"The authors, Dr Robin Crockett, University of Northampton, and Professor Gavin Gillmore, Kingston University, warn these levels are high enough to be dangerous even in much larger spaces, such as
whole houses." Worryingly even individual (military)watches can spike radon to an unsafe level.
I think radium as such is not very dangerous in this context, it's the decay product radon that has the potential to cause harm. The old watch forum saying 'just don't lick the dial and you're fine' is simply not true. If you are concerned about radon, you should measure the level in your home like the wise
@Dan S has done.