Oh NOOO!!!! That sounds nasty, I'm sorry to hear this and hope you manage to get rid of the stench before the next guest arrives. Personally I'd be more concerned with the thoughts of the new guest regarding the smell as opposed to the departing guest who caused it.
Re feedback, you can actually mention it to him in private if you don’t wish to say anything in the public review as might be a bit embarrassing and you can score him very low on cleanliness. He cannot view your feedback until he leaves feedback for you by which time it will be too late for him to change his feedback if he wishes to do so just because he doesn't like what you wrote.
If he doesn’t leave you feedback of his own within the 14 day period because he might be waiting to see what you write since he might suspects his stench may have been a problem and you were just being polite not saying anything to him in person, he will no longer be able to do so after this time.
When leaving feedback, there is a section where you can send a private message to the guest regarding situations as such, you can let him know the impact on you as a host, any cost involved and how it affects the guest checking in after him –it is actually good for him to reflect on how his inconsideration has a knock on effect; you also have the opportunity to flag it privately to Airbnb in this section, although I'm not sure that they will do much about a smelly guest.
You might want to consider adding a cleaning fee for future because unless you have to get rid of any bedding as a result of the smell, you are unable to claim against his deposit.
Good luck with the task at hand .....