....  The two cells are roughly C-sized nicads. This made me
wonder if a couple of ultracaps might be a reasonable
replacement. They might survive periods of disuse better...

Back of the envelope says that's liable to work like a charm!
Near instant recharge, too, with the right charging circuit.

Supercap cycle estimates tend to be in the 10^5 - 10^6 range,
too.

Of course I chucked an old Wahl cordless not long ago...

 Jack
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