You might be surprised to know that there are actual bathrooms on the Inca Trail. Early in the trail, you will have bathrooms that managed of by local villagers. For these bathrooms, you'll have to pay 1 Soles to use which is why it's important to have some change with you on the Inca Trail. Because these bathrooms are managed, they are generally in good working condition with a flush system. Do note that majority of the bathrooms are squat style which means you do have to get down to use it. If you are unfamiliar with squat style, take a look at this video. It is for a product that supports squat style pooping. Historically, squat style has been the norm and is more helpful when it comes to doing the #2 business. Many countries still use squat style toilets, but for those in the western world, many may be surprised by them.
As you continue on the trail, you will find that there are no longer a lot of small village stops and therefore no bathrooms. Bathrooms can be found at the camp sites. Because there are multiple people at the camp sites, you will find that these bathrooms do look a little unsanitary. Be prepared and always wear shoes. Sorry, but I would not recommend flip flops going into these bathrooms. Because the opening is on the bottom, a lot of people miss the opening and end up doing #1 or #2 on the floor. Some of the toilets may not support toilet paper so people sometimes just throw these on the floor. Gross!
I would recommend always bringing the following with you to the toilet: toilet paper, wet wipes, hand sanitizer and a light. In the first half of the trail, at the managed toilets, your 1 Soles will get you a few squares of toilet paper. Not usually enough which is why you need to bring your own. At the camp site bathrooms, there are no toilet papers at all. The sinks can sometimes be hit or miss. Either they are there or not so you need to be prepared to wash your hands. Because you are in the great outdoors, there is no light and when that bathroom door closes, you will be plunged into darkness.
The alternative to these bathrooms is the great outdoors. This is definitely easier for guys. We did have an incident where one of the girls peed and the pee ended up in someone's backpack as it was resting on a sloping hill. So just watch out where you do your business!
With regards to toilet paper and wipes, I would recommend buying something that is compostable. Because you may need to throw these out in the wilderness, you might as well use ones that are less harmful on the environment. In some of the trail areas, you will see lots of toilet paper clumped together.
I recommend the Honest Baby Wipes. The 72 count was enough for our 4 Days with plenty to spare and share.
For me personally, I kept my toilet paper, wipes, sanitizer and light in my light day back so that I could take it out easily. I then wore it in the front so that I could take out what I needed easily. I am also very sensitive to smell so wore my headband/scarf as a mask. No need for any other outdoor gear that they try to sell you. Keep it light and basic.