Hi and welcome. Not a good idea at all. Torts need to be in a safe and secure enclosure where they will have the right temps, uvb and humidity and won't feel stressed. They need access to a water dish (shallow terracotta plant saucer) to drink from and big enough for them to get in to self soak when they want to and absorb water through their vents. If you give your tort luke warm shallow soaks the chances are that he will pee and poop in that. What species do you have? I'll post the link for the caresheet you need. If you post pics of his enclosure and lamps you'll get good feedback on making it as safe as possible for him.
If you're going to take him someplace where you don't want him to poop and pee, then carry him in a small plastic tote. Tortoise tails need room for the poop to be able to come out. A diaper wouldn't provide that room. Not a good idea.
Reptiles are not like us...the opening in the tail for their urine and stool does not close tightly. Microbes in the waste would be able to easily get back into the body and cause serious infections if the back end of the animal were wrapped.
Also the smell. Reptile waste is super-odoriferous. Like super.
The healthiest condition for reptiles in the home is for them to stay in a secure, clean, climate-controlled enclosure that meets all their needs for territory, heat, light, humidity, food & water, and places to hide and de-stress. Animals left to walk on the floor get sick, injured, swallow non-food items, and don't grow properly. A secure tote can be used for car rides or other necessary trips outside of the habitat.
If you let us know what species of tortoise you have, someone can post the right care information.