Hi Billy, welcome to ETO!
Your 2.4v battery will consist of 2x 1.2v cells strapped together. They are probably in some kind of heat-shrink wrap.
If you can find out the dimensions of each cell you can identify what type they are, however if it says AA on the battery, without further information I'd say it is either 2x AA size cells, or the whole thing is AA size.
Here is a handy guide to sizes of cells: **broken link removed** however it's possible yours is another size not on here, in which case a photo and actual dimensions would help.
If you try looking for the trimmer itself on the net rather than just the battery you might have more luck.
Once you've identified the cells, chances are they are connected together by some kind of welded tabs. Your luck is in here, as you can get NiMh cells with the tabs pre-welded for you - you just need to solder them together into the pack size you need, wrap it up with tape or whatever.
Oh and to finish answering, mAh does not compensate inadequate voltage, you need to make a pack of 2x 1.2v cells in series. My own experience of replacing cells with higher capacity ones has been that the device was underpowered, even if the battery did last longer! So you probably shouldn't go much over the 750 (per cell). If you were to use a single cell, your charger would probably destroy it since its output is for 2 cells in series.
Hope this helps