IMHO Sony nailed this pretty perfectly 30 years ago on devices like the Discman: Have a footprint which can support a number of standard batteri(es), but engineer it so it also accepts and detects a specially-designed NiMH pack. When the special batery is present, allow the battery to be charged anytime external power is provided.

Now you have the best of both worlds: Economical rechargable use for the 90% of the time that the user's in their normal routine, and easily ability to swap temporarily to universally-available alkalines in exceptional situations.

Note: When I had one of these, I just used my own NiMH AAs and jammed a folded-up piece of cardstock against the detection switch, which worked perfectly fine.