Realistically, if you eat anything, you'll poop. Tail down your calorie intake to ~1000 calories at day -7, to -500 on days -6 and -5, then to 0 for days -4 through -1. Start eating again on day zero.
You won't have to poop during that time. Make sure to drink water, and i would add electrolytes to ensure you don't get any type of heart arrhythmia (unlikely on a fast this short, but intelligent anyway).
I don't know why you need to do this, but good luck. I've done week long fasts before and they're not too hard after the first couple of days. Ironically, eating well before the start makes it MUCH harder (you'd think it'd tide you over, but it just makes your body expect food) ... Hence, the tailing down over a couple days.