+/- 9V DC Power Supply
LM741 is a terrible op-amp for audio.  The NE5532 is something like 15 dB quieter, and still cheap.  Notes on Audio Op-Amps
You should be using rails as high as possible for best dynamic range. The mixers I work on are always ±15 V, because that's the highest voltage most op-amps are recommended for.
Power supplies with split center-tapped outputs exist, though I can't find any right now.  That's essentially the same thing as stacking two isolated supplies.  Also, you could always build your own with a center-tapped transformer and learn how to build linear supplies.   It's not too complex:  High Quality Audio Mixer - Stage 3 - Power supplies