If it runs on two batteries in series and you're willing to take a risk, you can get a 3.7V 14500 battery and then a dumb fake straight wire battery in there. Gives you 1.85V per-slot instead of the normal 1.5, which might be too much for the device, but beats the pants out of the 1.2V you get from NiMH AAs.
I got 14500s for my Logitech F710 game controllers, and then drilled a hole in the battery compartment of the controller to make them plug-in chargeable. I've only just played with them a few times - no guarantee this is a long-term solution, but it seems to work well for now.
Note that this does mean you'll have a bin of things that look like AAs but might cause a fire or melt if you put them into the wrong thing that accepts AA batteries (like the just-a-wire-fake-batteries have allcaps warnings about never ever putting them into a charger).
It actually gives you 2.1V per slot because a fully charged standard Li-ion cell is 4.2V. This is also sketchy because it will likely over-discharge the cell below 2.5V if not monitored carefully. Over-discharge makes it dangerous to charge the cell again.
Actual protected 14500s will be too long in most devices meant for AA, but it's possible to find protected 14430 cells marked as "14500" from some flashlight brands like Acebeam and Skilhunt. Those are safe with regard to over-discharge, but the voltage of a fully charged cell might still damage devices not rated for it.
I'd rate this modification as risky and only suitable for people with significant battery expertise.
Edit: saw the other comment mentioning 14500s with USB ports. These will be protected against short circuit and over-discharge, and are actually based on 14430 cells.
Ah, thanks! Good to know I dodged that bullet by blind luck. I had picked up a couple of USB-port charged version of one of those old chubby non-rechargeable lithium batteries that were used in early LED flashlights (CR2 I think) to resurrect some old steel LED flashlights I found in a drawer, and got funny fantasies about doing other devices this way.
I saw some articles and ads for doing it using 3.1V LiFePO4 batteries but I couldn't find any of those with USB charge-ports... I guess your warnings are why you're supposed to use the 3.1V Li-phosphates for that. So I went with the 3.7V LiIon because I really wanted that port.
I guess I dodged a bullet. Thanks for the warning. I actually did systems engineering as an undergrad (though I just work in software) so that makes me a bit overconfident with electronics even though I don't know jack about battery chemistry besides the basic theory. I'll be more careful on research next time I undertake this kind of project.
It seems like you might be looking for "1.5V Li-ion AA", which is a 14430 with a buck converter stuck on the end.
I have pretty much the opposite preference regarding charging: I'd much rather swap in a charged spare and stick the drained battery in a slot charger than charge batteries inside devices. There's no waiting that way.
I got 14500s for my Logitech F710 game controllers, and then drilled a hole in the battery compartment of the controller to make them plug-in chargeable. I've only just played with them a few times - no guarantee this is a long-term solution, but it seems to work well for now.
Note that this does mean you'll have a bin of things that look like AAs but might cause a fire or melt if you put them into the wrong thing that accepts AA batteries (like the just-a-wire-fake-batteries have allcaps warnings about never ever putting them into a charger).