you could make a 'dummy' patch on your module with volumes set to 0, then change patches via footswitch to your performance patch. Or, some modules will let you use a pad to switch patches.
If that's not an option with your gear, you could run your module thru a volume pedal and bring it in and out as necessary.
Or you can submix; I assume you're going to need some sort of mixer if you're running triggers and mics.
Might be a little tricky (but pretty much any option is going to be) but you could mute/unmute the trigger channel as needed.
Or maybe you could get one of those DJ A/B mixers and be all like wiki-wiki/boom snick/wiki
I think this is one of the main reasons most people use separate elements for hybrid kits; it's difficult to switch between mics and triggers on the same drums unless you've got a soundman who knows your material.
What I did when I used that kind of setup was to have a default patch for a typical acoustic tone and just left it on that patch till I needed the ethnic or electronic tones, and then I'd switch it to the appropriate patch via footswitch or pad.
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