Why don't you draw a schematic and attach it to your reply?
Audio signals use shielded audio cable where the shield is connected to the circuit ground at each end. The shield blocks hum and other interference.
You said "noise" but did not describe it. Rock "music" and loud cars and motorcycles are noise to me. Is your noise low frequency hum or high frequency hiss? Is your noise a POP sound each time you switch amps?
That is it... a pop sound when you flip the switch ! Is there any way to eliminate or at least reduce the sound ! Any advantage to grounding the metal enclosure to the sleeve of each in jack and out jacks ?
The pop sound is a coupling capacitor charging or discharging quickly. The output of the guitar and the inputs of each amplifier must be modified a little so that there is 0VDC on the switch.
If you switch while playing then a POP might be produced since you might suddenly switch at a peak level in the sound which is momentary DC. It is fixed by ramping down the level, switching, then ramping up the level back to normal.