AA-size Li-ion is called "14500" for anyone needing to source these. I'd love a mouse (or various other gadgets for that matter) that uses one behind a tool-free battery door.

Since the mice run 2xAA in series, you might get away with running one of those and jumping the other cell space.

If 3.7-4.2V is too much to handle, jump with a 1n4148 diode or two in series.

My Logitech G604 takes only one AA. I'm not sure the advantages over NiMH (lighter weight, higher capacity) are worth soldering in diodes especially when the efficiency loss would negate the capacity advantage.

I just went and took mine apart, it's a Logitech Performance MX, and it uses a NiMi battery: 1.2v, 180mA, 1900mAh.

The battery door pops on and off with a fingernail.

They really do look like dead-ringers for AA batteries. I bet you could run the mouse off of a regular AA as long as you didn't try to plug it in!

That is an AA battery. A web search suggests those shipped with Panasonic Eneeloops, which are probably the best-regarded NiMH AA for general use due to their shelf stability and long service life.