If you dropped your CD player, you might contaminate the local area. There would be no explosion.
The linked article was talking about tritium-powered batteries, which are different from traditional plutonium-powered batteries. It doesn't operate from the heat of decay, so it would not be a thermal battery. If it was a thermal battery, you might not want it in your CD player since thermal batteries are only ~5% efficient and therefore can get quite hot.
I have been following tritium battery development for awhile and I see a major difficulty in retaining enough tritium to have a useful energy density. Typical 10-year tritium exit signs only hold 1 milligram of tritium in the entire sign, which produces ~1 milliwatt of energy before conversion losses. If you want a battery that can put out a more-useful 1-watt or 10-watts of electrical power, you are going to have to find a package that can hold seriously compressed tritium gas without risk of breakage. I have seen a suggestion that hollow, thick-walled glass spheres the sizes of marbles might be usable. The trick would be to figure out how to manufacture these economically with high-pressure tritium gas captured inside.
Anyway, I think part of the big picture is that the American military would be very interested in a battery that never needs replacing. (Supposedly, the field service life of the current lithium-ion batteries in deployment is measured in months. The heat in Iraq and Afghanistan is probably one culprit, as well as a poor battery-maintenance culture. Of course, since a tritium battery never needs servicing or charging, it would be ideal for addressing the latter problem. Heat can sometimes affect transistor performance, though, so I think the former problem might possibly mean larger tritium batteries would be needed for deployment in high-ambient-temperature environments such as the Middle East.)