Yeah sure, technically, we use around 7.4v batteries because it's the good voltage for the screen and it does work for the n64. so if you have 3.4v batteries, solder two of them in series (which means You connect the + of one with the - of the other than the + and the - remaining connects to the circuit) will get you 7.2v, which is enough. Later you can solder two of these pack in parallel so you double your power time. Be sure that the batteries have a protection circuit, because if it doesn't, it will charge until it explodes because they don't have limit. The better way to do that, if you're not to familiar with portables and things is to buy camera batteries, like canon. I'm not sure it does have a protection circuit but the charger does, so it's the same at the end.(Plus these batteries are already 7.4v)
The problem is that you will have to do your 3.3v line already, because you cut the port. Look in the n64 mega-sticky, for the how to get 3.3v topic. You will need some electronic, but it's not that hard to do, just be sure that you really output 3.3v for the line, if you output too much, your n64 will be fried.
And for the power switch you just cut, Just put a on/off switch at the beginning of your circuit( on the positive cable, between the batterie and the n64) and solder the pins of the original power switch together following this instruction:
Under the board, where the power switch was, you have 8 pins with numbers. Just solder 1-2 together, then 3-4, 5-6 and 7-8. You can solder them from the top of the board too, doesn't change anything. That way, the n64 will always be powered on, but you can cut the power from the batterie with the switch you soldered just before.