It doesn't.
What you believe to be the "input" is not an input. It is the output. Although you physically plug the guitar cable "into" that jack, it is in fact the signal output from the guitar to the amplifier. Also, it would be good to avoid calling it "power". It is your audio signal from the pickups, not power. True, even though the audio signal from your pickup has measurable power in the milliwatts, it is distinguished from actual power signals in circuits which provide operational power to the system.
The signal flow in this diagram is pickups, to volume controls, to switch, to output jack. The tone control is in parallel with the output and forms what is called an RC (resistive-capacitive) resonant circuit. This resonant circuit is what affects the tone of the output.
BTW, this concept is the same for all electric guitar circuits with a tone control. The tone control will be in parallel with the output. The exact physical point of connection may vary, however, depending on the number of pickups, the number of volume and tone controls, the switching, etc.
As for replacing the box switch, you may not be able to do it. I have one of those in my Jackson and I explored replacing it with a more standard, Strat-type switch. However, it would be too deep to fit in my guitar unless I routed deeper into the body for it. Ray suggested this may be necessary in an earlier post. I didn't want to do this for fear I'd leave insufficient support for the switch (the Jackson has no pickguard, just the body wood). So, I just blasted my switch with electronics contact cleaner and continue to use it to this day and it's been fine.
But, your OP stated that the guitar buzzes when you have the pickguard loose. Does it buzz when you fasten the pickguard back to the body, thus providing intact shielding?
If it doesn't buzz with the pickguard installed, congratulate yourself on your shielding job. It's doing what it is supposed to do!
