Power for portable project
Taking a look the unofficial SNES schematics will be hugely helpful here.

Referring to this document reveals that most of the SNES runs off a 5V supply generated by a 7805 regulator (U12). Replacing this regulator with a more efficient switching regulator will significantly improve your battery life.

However, the SNES also expects a 9V supply to be available on VS. 7V is actually not sufficient for this rail; you will likely find that sound is distorted or muted when running on a 7V supply. You will need to either use at least 3 cells to supply enough voltage to this rail, or use a boost converter to provide this supply. (The draw on this rail should be minimal; it's just running a LM324 quad op-amp and a few analog components in the amplifier.)

Using a boost regulator, especially from 3.7V, is not advisable. The efficiency of boost regulators is often not very good, and would be compounded when running a second regulator for VCC. You're much better off driving two separate buck regulators from a higher voltage, or potentially generating 5V with a buck regulator and 9V with a boost.