Jasper, you can save the presets on your H9 in bypass mode, so that when your MIDI controller recalls it, it will be called up in bypass. You can then engage it on the H9 itself.
If you want, you can dedicate a button on your MIDI controller to send a CC message to the H9 to activate or bypass it, but you’ll have to assign a CC# to the “toggle between Active & Bypass” function in the H9. There’s a couple you can experiment with actually. You’ll find them on H9 Control in the “Assign MIDI CC messages” in Pedal Settings.