If coming from the router, the fizz is likely to be from the -9 volt power supply. You could remove the 1044 charge pump voltage inverter and connect two 9 volt batteries up as a test, one for the +9 volt power, and other other battery for the -9 volt power. Or maybe use a battery just for the -9 volts and still use the wall wart supply for the +9 volts. Or use a bench power supply instead of the 1044 for everything.
In other words, just see if the 1044 is causing the problem. Not that it is likely to be defective although it could be. They just don't supply very clean power, or very much current. They are popular for use in some guitar pedals, but guitar pedals are typically built to a price point and dual external power supplies are expensive. And, most guitar players don't notice the difference anyway.
You could also try dropping in a LT1054 charge pump instead of the 1044.
http://www.ti.com/lit/ds/symlink/lt1054.pdf They are a little better than 1044 versions.
Also, it helps to use low ESR (Equivalent Series Resistance) capacitors with charge pump power supplies. Aluminum Organic Polymer Electrolytics with ESR or 40 milliohms are available and not too expensive. Normal electrolytics, either aluminum or tantalum, typically have ESR values up around 25 ohms or maybe even higher. Maybe 500 times worse than Organic Polymer caps. That would be C3, C4 and C5 on the schematic.
Also, shorting one of the opamp outputs when one of the input jacks (applies to input B only) is plugged in could worsen any power supply problem. Perhaps a good idea to put a resistor in series with that output or with the ring connection on the input jack. 10k would probably be plenty, and 1k might even be enough. Probably somewhere around there, a few k-ohms. It would probably be better than relying on current limiting on the opamp output which might waste a few 10's of mA's of power supply current.