This national geographic post discusses many mammals that sneeze. It doesn't come right out and say _all_ , but suggests most mammals have a cough and sneeze reflex:
> Mammal coughs and sneezes come from throat and nasal passages, respectively, says Bill Milsom, a comparative physiologist at the University of British Columbia.
>
> Mammals, he says, are the only animals that process food in the mouth by chewing. In other types of animals, like reptiles, "food is swallowed whole or by chewing, and breathing is suspended during the event."
The same expert discusses non-mammals that sneeze, marine iguanas and fish.
You don't even need nerves or muscles to sneeze, per this Cell Press article
> Sponges 'sneeze' without the benefit of nerves or muscles