Is possible to figure out if a battery is NiCd or NiMH?
NiCd cells are much more dense then NiMH, so if you have two cells of the same size (e.g. AA), it's easy to determine by "hefting". However, with a sealed battery, this may not be so obvious. You could determine the density by Archimedes' method, but you probably don't want to get the inside of the battery pack wet (unless you can thoroughly dry it), to prevent electrolytic corrosion.

BTW, NiCd cells are much more resistant to damage from over-charge and from complete discharge than NiMH, and are still widely used in portable power tools and other high-drain applications. NiMH provide more total energy by mass, and more environmentally "friendly'.