R. Connor Montgomery — CONELRAD
Vostok watches should be safe as they were made from 1965 to the present and do not use radium as the lume. It's the vintage ones from the '50s such as this mammoth Zlatoust Diver Watch that has radium.
Promethium was also used in luminous paint. While it is still radioactive, I believe it is nevertheless much safer than radium.