Aside from opening it of course. I'm not sure if this is the right place to ask this but I have a rechargeable battery pack for an Xbox One controller and the info on it says that it's a sealed nickel cadmium battery but it also has a recycle symbol with "NI-MH" written underneath. The company's website doesn't seem to have any customer support and I tweeted at them on Twitter but haven't received a response. If it is NiCd, I'm surprised that any batteries of that type are still made. If it were Ni-MH I'm sure they would say it on the packaging. I think I read that NiCd cells don't have a large voltage drop until the end of the charge, so I suppose I could measure that. Does anyone have any suggestions about the battery type or know of a better place I could ask this question?
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'.