Atmega 328PU and SNES Controller at 3.3v

So I have the Project on building my very own SNES-Style Classic Controller out of a original SNES Controller, a Wii-Mote Extension Cord, Atmega 328 PU with Arduino Core.

Everything works when using the Arduino Board, as it has every Voltage (5v and 3.3v).

But when It comes to integrating the ATMega328 in to the SNES Controller Case I dont know if it is possible to run the Atmega and the SNES Controller at 3.3V and how Stable it is. As the Wiimote only uses 2 AA Batteries.

This is the Code I use as base, but I removed everything that is not SNES related. So it is really compact and small.