Nuclear physicist here!

I agree with the general consensus in the comments. Alpha radiation from radium is easily stopped by a few centimeters of air, a sheet of paper, and even the dead layer of cells on the outside of your skin. So long as you don’t eat, inhale or inject the radium, you’ll be fine.

I wouldn’t keep it on your person for an extended period of time though - for example carrying it in your pocket every day, sleeping with it under your pillow, etc. Store it somewhere safe and not immediately next to your skin; the back of a drawer or on a shelf would be fine. Feel free to use it or show it to people from time to time. That’s a neat piece of history to have!

Assuming the majority of the material on it is still Radium, the good news is it's mostly undergoing Alpha decay - which can be stopped by something as simple as your skin. Depending on the decay chain, there's also probably a bit of Beta decay in there, for which a strong metal box will probably suffice.

But the real point here is that 10 uSv is the radiation equivalent of being alive for an average day, so brief exposure is unlikely to cause real injury. But here are some things you can do if you're still concerned:

• Limit time exposed to it. It's okay to take it out to show to friends and family, but otherwise keep it somewhere people aren't likely to be nearby.

• The aforementioned metal box.

• Wash your hands thoroughly after handling, and/or wear gloves. It's unlikely, especially if the radium-painted parts are under glass, but possible that radioactive materials could end up on your skin. Washing hands should prevent this.

If you've heard of the "Radium girls", the thing that really made them sick is that they were licking radium-coated paintbrushes, causing radioactive material to end up inside their bodies. Since (I presume) you're not licking the compass, you're much less at risk.

I wouldn't worry about it - you are largely only going to harmed if you ingest any flakes of radium paint. If the compass is sealed and you use gloves when handling it you should be fine. If you wanted an extra level of security you could buy a perspex display box to put it in so, even if it wasn't sealed and paint was flaking off it, no-one close to it would come in contact with it.

Have a read of this for more information.

I spent years working with radioactive materials in a lab and, as long as you aren't careless it's not a worry - there were much more dangerous things in there that genuinely scared me (like hydrofluoric acid).

You reminded me of this:

https://xkcd.com/radiation/

I don't think you'd need to do anything too extreme for that low of a level of radiation. If you want to keep it, it should be fine in a drawer in a dry, well-ventilated room. Just don't hold it bare-handed for extended periods, and don't somehow swallow a piece of it, and you should be fine. Also wash your hands after handling it, as you may get radioactive particles on your skin. If you've got children in your home, it might be a good idea to make sure it's inaccessible to them, either somewhere they can't access or somewhere with a lock.

If you'd rather not hang onto it, I believe you can contact the EPA, who can refer you to a local facility that can properly dispose of it for you. Or maybe check out some local groups to see if there are any collectors that would prefer to take it off your hands, as they may be more likely to preserve the piece for you, if it has any sentimental value to you.

leaded glass display case?

You might try asking Mackie about this. Not sure if they're still active or maybe lurking, but they literally have a lil' community for old uranium glass products which may mean they have just the sort of insight you're after.