You could use a puppy playpen that has a grated floor. That would keep the pup up off the ground - no contact. People at dog shows use these. You can keep a bucket of water with a toilet brush and disinfectant to clean the grate. They usually come in a 3' by 3', or a 4' by 4' size. You can get them with or without a top. If you have the top, it opens to facilitate cleaning, but it also keeps the pup contained without risk of him escaping. With the size of the playpens, it would give the pup plenty of space to move about while you were sitting out at your campsite. No need for his feet to touch the ground.
I agree with Dr Doug, the age and vaccination status of the pup would be an important factor.
When we first started RV'ing, I had a 15 y/o dog. I really hate taking a senior out at rest areas. I think they are a den of contamination. I tried buying one of those litter trays, hoping they would learn to go in the litter pan in the RV. With his age, he had to go frequently.
That failed - as he thought he should EAT the litter pellets. I then tried just putting one of the puppy piddle pads in the doggie litter pan. That didn't work either.
I think if the day comes that we get another young puppy, I would like to try to litter train them/ combined with normal outside housebreaking. Just so they could use the litter pan in a pinch when traveling.
Just my two cents.