After neuter, pooping outside the litter box
After my cat got neutered I changed his litter as to not get the regular litter in the incisions (to paper litter).
About 2 days prior to going back to the vet for a checkup, he started pooping outside the litter box - not far, directly outside it. He will still urinate in the litter box but not poop.
If he poops in the morning for example, he must've pooped and then either finished in my bedroom or brought a piece in there because he woke me up to tell me about it. When I find the poop, I usually put them back in his litterbox and he follows immediately to cover it.
He just had his checkup after being neutered this past Tuesday, and is perfect... running around, eating, playing - everything he did prior to being neutered.
Should I change the litter? The litter box? He's such a good boy, and personally I think this is more behavioral than medical.
If the vet says he's healthy and gives no medical reason for this, I'd guess that he's not happy with the litter change.
Paper doesn't provide a lot of odor cover up, and I think it's possible that he's not able to cover up as well as he'd like.
Another indication is that he's pooping right beside the box, which can signal that he's not happy with the box conditions.
Based on that, I'd start by going back to the litter you used before (assuming that's OK to do per your vet) and see if things change. Another thing I'd do is get a second box and put it in a different location (following the "one plus one" rule).
I hope that helps. Please let us know how it goes.