If you need to walk around a lot, it'll be tougher to do it on am empty stomach, but not impossible. You have plenty of energy stores to last 3 days unless you're significantly underweight to start with.
You will not be able to eat your daily allowance of calories for three days and not need to poop during that time. It's just not a thing that's going to happen for you.
If you are determined to eat and not poop, eat protein bars, and take an anti diahrreal (e.g., Imodium). You won't poop, but day 4-5 will be awful.