I was aware that there was a radiation issue with the faded 'glow-in-the-dark' paint. Like your compass, the 'crosshairs' on mine are a faded beige colour.
Radium (Ra) decays by the loss of an alpha particle to Radon (Rn). An alpha particle is basically a Helium (He) nucleus, i.e 2 protons and 2 neutrons but stripped of the 2 electrons. As such, alpha particles readily ionise and can therefore be blocked by just a centimetre or two of air. As Radium is a solid, the main risk is if you were to inhale any particlles, or touch them. Even then, they would need to undergo radioactive decay whilst in contact with you to cause any problems, The half life of Ra is around 1600 years but that of Rn is just 3.8 days. Ra is a gas and also an alpha particle emitter. It is therefore easily inhaled, with a higher risk of the alpha particle ionising in contact with the lung.
Radon decays to Polonium (Po), which as well as being radioactive, is also extremely toxic.You may recall the death of Alexander Litvinenko in London back in 2006. Allegedly poisoned with Polonium by a KGB agent.
But, before we get too gloomy regarding the Radium on our compasses, we need to consider the amounts and these are tiny. I watched a documentary a couple of years or so back. In this, people working in aircraft factories during WWII (where the paint was splashed all over certain aircraft parts) were painting it on their faces and hands (being unaware of the danger). They received massive dosses of radiation - you can guess the consequences.
A couple of years ago I went to an airshow and one of the stands had several of these WWII compasses for sale. If there was any significant risk from these items, I very much doubt they would be allowed to be traded.
So, enjoy owning your compass. Just treat it with a little respect.
Sorry for the Science lesson, but I'm a Scientist and I loooooove Science.