You already
made a thread about problems about getting 3DS batteries in Venezuela – and got
this post as an answer. Fitting and connecting some small li-ion battery seems like the best idea.
It is worth noting that the CTR-003 battery is pretty common and will stay for a while. As far as I know, it is also used for both, the Wii U and the Switch, Pro Controllers.
While 3 NiMh cells have a similar voltage to one li-ion cell, you can't interchange them. Charging methods greatly differ between those two chemistries¹. Estimating charge level by voltage doesn't work on nickel based batteries.
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¹ Li-ion is charged with constant current until a defined max voltage is reached. After that the current is gradually reduced in a way the voltage stays constant. Once the current goes below a certain value the battery is defined full.
NiMh and NiCd are charged with constant current until a sudden small drop "–ΔU cut-off" in voltage is noticed. After that the charger may go to very weak trickle charge (at least for the old NiCd, the newer cells are a little more delicate in this regard).