What I would do in this situation would be a 4-day fast. It's not for everybody, but you might want to at least consider it, because it's definitely doable, and some people even claim it's healthy (disclaimer: I am not a medical professional, don't take medical advice from random people on the internet).
To prepare, I would suggest switching to OMAD (one meal a day - effectively you will be fasting 23h every day) up until the trip. OMAD will help your body adjust to long periods of not eating. To be successful with OMAD, you need to ensure that your single meal will cover your daily calorie and nutrient needs. There's a bunch of resources about it online if you search.
Eat your last meal 48h before the trip - this will give you a chance to empty your bowels before you leave. Every day, make sure you drink enough electrolytes + take multivitamins. On the final day of your trip, it should be safe to have a SMALL meal (do not overdo it, you can hurt yourself by eating too much after a fast) - it should take your body over a full day before you'll need to poop.
How long do you have to prepare? Personally, when I first started doing OMAD, it took me over a month before my body became adjusted to fasting. But now, it just feels completely natural.