Earlier quoted context omitted.
According to the article, the energy is generated by alpha particles, which are in principle a very dangerous form of radiation. It's not clear to me, though, whether the radiation stops as soon as the fusion does or not.
Up until a decade or two ago, tritium--which emits alpha radiation--was commonly on wristwatch dials, precisely because they were not dangerous. Alpha radiation is easily stopped; it's only dangerous if you breathe it (or drink it, if that's even possible).
It might also be worth pointing out that "It must be safe! They even put it on wristwatch dials!" is not, historically, a sound argument.