You can assign a global MIDI CC control # to each effect, then use a button on your controller to turn that on or off.
For my Garcia preset, I have the following eight controls on the Ground Control Pro:
Pitch (octave)
Wah 1 (Mutron)
Phaser (phaser with expression pedal rate)
Drive (Dist +)
Wah 2 (wah-wah with expression pedal as controller)
Filter 1 (+6db boost)
Delay (delay with expression pedal for level)
Tap tempo (tap tempo for delay)
Once you set those up, the controller will turn on or off the effects block on any preset in the AxeFX. So no need to change presets at all, the Garcia preset has all the effects I ever use on it, I never change presets at a show.
Without a foot controller, you could set up a preset for each version with the various effects on or off as desired. However, if you are using an effects loop on the guitar, you can have your clean preset working with the effects loop off, and then use the switch on the guitar to bring in distortion, or whatever preset you're working with.