I'm not sure how I would go about the same thing (I have already learned some terms here - but I am still a complete beginner), but if you have a higher voltage source, and want to step it down to e.g. 2v, you don't necessarily need to build any circuit. You could buy a cheap circuit from eBay.
Just search for adjustable step down module (they are also known as buck - voltage step up would be known as boost). These types of modules should allow you to set any output voltage desired with a screwdriver (for the miniature ones).
Charging is another matter. If you have a battery pack with a plug, say those made for RC planes/copters as recommended above you could possibly solder a compatible plug (same as the charger would have) to the input of a step down (and the output would be connected to the device battery input). Then when the battery is empty, take the battery out, plug it into the charger to charge... and plug it back into the module once full (in case the buck output voltage depends on the input/battery voltage, I would also configure the output voltage on the step down module when the battery is completely full, so that it couldn't output too high voltage at any point).
I am not sure how to reuse the battery case. I would check some YouTube videos of the disassembly process first to see what to expect, but it's surely easier and safer (while maybe less aesthetically pleasing) to avoid using the original case if at all possible.