While there is no MIDI Designer feature to shut off subcontrols in performance mode, you can usually achieve the same thing using Channel Changers. By changing the channel of the subcontrol to something that your MIDI target is not expecting, the control is essentially off.
Setup
One supercontrol with two subcontrols.

Setup for Sub 1

Instructions In Detail
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Set up is a knob that controls two other knobs: Sub 1 and Sub 2
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Add a knob and call this knob "Hidden"
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Change its type/subtype to Channel Changer. Accept the defaults for Channel Changer conversion.
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Set "Hidden" knob to "Hide in Performance" (in advanced)
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Add Sub 1 as a subcontrol to "Hidden"
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Create a toggle button called "Off"
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Make it a supercontrol of the "Hidden" ocntrol
Switch to performance mode. The "Off" button will change the channel to "16" for your control.
I Don't Use Channel 1!
Set the MIDI minimum on the Channel Changer Super ("Hidden") to be the channel number you need (it's 0-based, so Channel 4 would actually be called 3).