The battery restrictions apply only to the large lithium batteries such as used in laptop computers, or commercial video cameras and lights. These have the potential to get hot enough to start fires when rapidly discharged if for example the terminals are short circuited. They are allowed if in a proper, unit specific case designed to protect against accidental discharge.
Batteries in the AAA to D sizes are unrestricted, regardless of what type they are.
I suggest you keep batteries in lights with a paper disc at one end of the stack to break the circuit so they can't accidently get turned on. Spare batteries can be rolled in paper cylinders, to protect theit terminals from shorting. Rechargeables are best carried in the light or charger unit.
Avoid carrying things with circuits sich as portable hard drives in checked luggage. While they're allowed, batteries and circuit boards showing up in the X-ray can trigger a hand search, and the increased risk of loss that entails. (no offense to the TSA folks)