Beta is super-easily stopped. A piece of cardboard or tinfoil reduces it dramatically, or stops it completely, depending on energy per particle, total flux, etc.

I've a Luminox watch, the dial is visible in darkness all the time, you don't have to "recharge" it. It works by having small amounts of tritium decay within luminescent tubes. The radiation produced is beta - but the levels of radiation outside the watch are essentially zero. The body of the watch is enough to contain it.