That no battery mod can be done, but it's not something like directly connecting the AC charger to the battery terminals.
There's retrofitting a Li-ion battery from another electronic device.
Personally, I would bite the bullet and buy a compatible 3DS battery. Do you have any friends or relatives who live another country in Europe or North America? If you do, the next time your mee-maw and mother send each other Turkish exclusive teas, spices, and whatnot, pay them forward to buy the 3DS battery and ship it in the family care package. Check my signature for battery options.