Step up voltage?

[Steve Conner]

A linear power supply just means one that isn't switched mode.

The "linear" part originally was the regulator stage which would run as a linear amplifier, basically starting with too much voltage and using a transistor as a variable resistor to throw away the excess. In contrast to a switching regulator which chops the transistor on and off, creating a series of pulses that average out to the desired voltage.

One advantage of a charge pump is that it doesn't require an inductor. I'd feel uneasy about using inductors with high frequency currents pulsating through them, right next to guitar pickups. At least HF magnetic fields are easier to shield against than line frequency.

[km6xz]

In this case we are talking about a 82 microhenry self-shielding smd part running at 600khz. I would be very surprised if you could detect the field a few inches from it monitoring 600khz, let alone a guitar amp that has a low pass response 6 octaves below the fundamental of the oscillation. Advantages of a boost regulator with inductor, as tiny as it is, is superior load regulation and higher efficiency, with a bonus of fewer parts.
In either case, what is sought, can be done without much expense or work. I like the phone battery option because they have higher power density than a rechargeable 9 volt.