Well, the rechargeable batteries that are least likely to blow up in your face are the ones with the old-style NiMH (nickel metal hydride) chemistry that they use in rechargeable AAs and such. They have lower energy density than the lithium chemistries, so there’s less there to explode. They’re pretty inert unless you stuff them into a charger that doesn’t work properly—a busted charger can set just about any battery on fire. (Why is the NiMH chemistry still used for AAs? Because the normal voltage of a single NiMH cell falls nicely in the middle of the voltage discharge curve of a single alkaline cell. Lithium chemistries don’t have that property.)