There is no reason you should have to nag him. you are forbidden from this litter box duty!
So, as soon as he empties the old stuff out, pour a quarter cup bleach in the box and run, tell him to spray water in it and start scrubbing! When his eyes burn from bleach mixed with pee (ammonia) he'll maybe understand why you can't do this duty. I use bleach. I don't have a hose or a bathtub. I have to pour a bucket of hot water into the litter box in my tiny bathroom, then add some bleach and wait for 10 minutes for the stuff to soften. And yes, my Scamper has once peed on the floor waiting for me to be done with this chore! (I like air drying, but only because it seems more sanitary than using towels - don't know where I got that idea.. probably an old nursing thing...! but NOT necessary! towel dry and get it down!)
Are you using scooping litter?