my understanding is that the nominal voltage you get out of a cell is always dependent on the chemistry it’s using. alkaline battery cells are always 1.5V until they run down. even a 9V battery is actually six little 1.5 V cells in series in its little rectangular box. NiMH cells are 1.2V. Lithium batteries are actually a variety of different chemistries, but i think all of them have upwards of 3V nominal voltage, so they wouldn’t make a good drop in replacement either without some kind of voltage regulation circuitry.
are those not identical? regardless, i’d recommend checking out a vertical mouse. my partner works with a mouse a ton as a 3d artist, and swears by them.