Unless you're going to lick the glowy part or grind it into a powder and ingest or inhale it, then any radium isn't going to be a problem.
It's in a stable state, it has a very long half-life (1600 years), and is present in very small amounts (only a miniscule fraction of the paint was radium to start with). Radium is a problem if ingested or inhaled because it is taken up by the bones.
If you're concerned, then get rid of it to the tip.
Otherwise, enjoy it for what it is. Be aware that any vigorous cleaning could be a risk, but that's all.
You will get more radiation dose from your computer screen than you will from that clock.
Edited by RobJP on 25/04/2018 at 17:45
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