The actual dose you receive from working with lume is probably relatively insignificant, even if it comes in contact with your skin.
Ingesting or inhaling lume on the other hand presents a somewhat greater risk, particularly if you do so regularly.
If you were to remove and store all of the lume from every watch you ever encountered, and then swig the resulting concoction, the acetone would be a more immediate hazard.
Here is a chart of relative doses that brings some perspective to things.
https://xkcd.com/radiation/
It is factually correct to state there is no such thing as a safe dose of ionising radiation, but since you are being bombarded with the stuff naturally, the additional risk of working (sensibly) with lume is relatively low.
Flying from LA to New York is more risky I would suggest, and even then, the risk is pretty low.