the differences between the types of discharging regarding NiMh and Nicad is, Nicads don't last as long as NiMh's but they discharge desent is a gradual drain until nothing, and they have to be completely discharged or they will build up what is referred to as a "memory" and will burn a cell, or cease to work at all. NiMh's on the other hand last longer and don't exhibit the memory effect and/or not as bad as Nicads, but when they start getting low on juice, they don't gradually desend, they get to the last of their nominally functional point, and then drop off like a rock. so yeah, it will appear as though you have juice enough to run something, and then out of nowhere, none at all...lol
those 3.6 or 3.7 volt lithium-ion rechargeables could replace your existing 3 x 1.2 volt, or 1.5 volt battery configuration with one battery, but you would have to modify the device with some way of hooking up the battery as a power source. getting some really small tools and a trip to radio shack could cure your problem, if you feel up to it. if not, I'm sure if you look around enough you can find a reputeable electronics repair shop that would be more than happy to do the modification for you. it's not that difficult.