But seriously, can you replace a NiCad battery with a NiMH one?

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NiCd and NiMH cells are similar in their characteristics. If one is willing to operate them somewhat sub-optimally (primarily in detecting "end of charge"), you can interchange them. The 1xx series charging circuits are not particularly sophisticated (which is why the batteries wear out a bit sooner than they otherwise might), and so a NiMH substitute probably works ok. There's a slightly greater chance of overcharging NiMH cells, but if you don't leave it plugged in all the time (i.e., let it discharge once in a while), you should be fine.