[colejohnson66]

The 3DS is an excellent choice due to it’s hackability and pretty decent processor(s). However, OP also asked for a replaceable battery. I’m assuming that means something like AA like the OG Gameboy had. Does anything come that way anymore?

[shorts_theory]

No, I don't think single use batteries have been on handheld consoles since the OG GBA :-) But the 3DS/XL's Li-ion battery is pretty easy to replace with a screwdriver.

[bentcorner]

I take OP's statement to mean a battery that can be easily replaced without taking the device apart.

I'm pretty sure you can replace the battery on (most? all?) 3DS models. At least on my New 3DS it's user serviceable.