The trick with a litter box is to clean it at minimum, once every day, but preferably anytime the cat uses it, scoop that out and into the garbage, then keep the garbage carried out often.
Just get a handheld dust buster to suck up the errant litter or a little whisk broom and dustpan.
I had a semi-disabled friend and their cat traveling with me for a few days. We just used the shower for the littler box, it was easy enough to sweep up loose litter with a little broom and dust pan. Every time I cleaned the box, I took the doggy for a walk to the dumpster with that and whatever other garbage we had, so the cat was happy, the dog was happy, the friend was happy and my garbage pail was perpetually emptied.
We only used the shower area for about 5-10 minutes each, once a day. In that case, we moved the litter box, swept out the litter. After showers, I mopped up the shower floor with first the used washcloth, then second with a paper towel, then the litter box was returned to the shower where it lived for the next 23 hours and 40 minutes.
They had the coolest cat I've ever met, big kitty, about 20 something pounds but not fat, just big boned with super soft fur. He was so laid back, just watching my 6 pound dog bounce around, several times leaping over the cat who was laying down and he barely batted an eye. I was amazed.
However, the cat had "visited" in my motorhome several times while parked in their driveway. So when we loaded him up to go on a trip, he was a tad confused but not stressed, as he had already had a chance to explore the RV many times before.
So... it's always good that pets get to explore the RV some before you head down the road. The more visits before the trip, the better for all of you.