What a sweet, beautiful boy! He's obviously quite enamored of you. 
First - a quick answer on a bath. Every vet/clinic/etc I've ever seen says no getting the incision wet for 14 days.
I didn't see an answer to @Furballsmom as to whether he's eating or drinking anything at all. It sounds like the steam is helping him breathe, and often when kitties can't breathe well they don't want to eat either (like people - scent helps the drive to eat). If he hasn't eaten or been drinking - I would definitely be even more concerned about that then him not being clean (although cats often don't drink or eat too much for the first 24-36 hours post-surgery - -but most vets will say if they're not eating by day 3 - - -they need to be seen). BUT - - often it all ties together. It sounds like you definitely know kitties - so I'm sure you know how clean they usually like to be, and often if they're NOT cleaning themselves, it indicates something's not right health-wise. Have you monitored his food and water to know what's going in - - and the litterbox to know if anything's coming out? Since obviously you can handle him and really feel around - - does he feel dehydrated (do you know how to check? Here's a youtube video that shows how: )? If he IS dehydrated - even though it sounds like you may be a bit of a drive to get him somewhere (and it sounds like probably another vet other then the one at that clinic - - -who didn't seem overly helpful!) to be checked over - - I wouldn't mess with that for long.
If he's eating, drinking, and starting to act better and clean himself, it could have just been a reaction to the stress of the drive, the pre-surgery handling, etc etc. And - like most everyone above - I wouldn't recommend soap at all at this point. I think cleaning him up is a wonderful idea - - I often find (again - like people) cats will perk up just because they finally feel clean. But I'd only use a washcloth that's damp - not soaked - with warm water. And make sure he stays warm after he's been cleaned - - I'd sit in a bathroom with him and a space heater for awhile if possible (I never leave a cat alone in a room with a space heater). It's possible you can use a hair dryer on VERY low heat and low speed (and use a diffuser if you have one) - - but often hair dryer's are SO terrifying for cats, which is the last thing the sweetie needs. I also use Petkin Bamboo Eco Pet Wipes on ours when need be - - they're very gentle (and even Walmart carries them). They're like a baby wipe - not super wet, so he won't chill. I even warm them slightly in the microwave on SUPER low particularly if I'm using them on kittens.
And most of all - trust your senses. If he doesn't seem better, or even seems worse, and you just have "that feeling" -- get him in somewhere. I've learned to trust my "spidey senses" on this kind of stuff. So I hope he feels better - I'm so glad he has you to care for him (and care for his world in general in that he won't be making babies - - -or fighting for territory/females/all the "good stuff" that comes with unneutered male kitties!) and love him and make sure he's ok. So few people are willing to go through that much love, care and effort for what they'd call "just a stray cat." Obviously he's more than that to you -- - and it looks like the feeling's vice versa
Keep us posted!
First - a quick answer on a bath. Every vet/clinic/etc I've ever seen says no getting the incision wet for 14 days.
I didn't see an answer to @Furballsmom as to whether he's eating or drinking anything at all. It sounds like the steam is helping him breathe, and often when kitties can't breathe well they don't want to eat either (like people - scent helps the drive to eat). If he hasn't eaten or been drinking - I would definitely be even more concerned about that then him not being clean (although cats often don't drink or eat too much for the first 24-36 hours post-surgery - -but most vets will say if they're not eating by day 3 - - -they need to be seen). BUT - - often it all ties together. It sounds like you definitely know kitties - so I'm sure you know how clean they usually like to be, and often if they're NOT cleaning themselves, it indicates something's not right health-wise. Have you monitored his food and water to know what's going in - - and the litterbox to know if anything's coming out? Since obviously you can handle him and really feel around - - does he feel dehydrated (do you know how to check? Here's a youtube video that shows how: )? If he IS dehydrated - even though it sounds like you may be a bit of a drive to get him somewhere (and it sounds like probably another vet other then the one at that clinic - - -who didn't seem overly helpful!) to be checked over - - I wouldn't mess with that for long.
If he's eating, drinking, and starting to act better and clean himself, it could have just been a reaction to the stress of the drive, the pre-surgery handling, etc etc. And - like most everyone above - I wouldn't recommend soap at all at this point. I think cleaning him up is a wonderful idea - - I often find (again - like people) cats will perk up just because they finally feel clean. But I'd only use a washcloth that's damp - not soaked - with warm water. And make sure he stays warm after he's been cleaned - - I'd sit in a bathroom with him and a space heater for awhile if possible (I never leave a cat alone in a room with a space heater). It's possible you can use a hair dryer on VERY low heat and low speed (and use a diffuser if you have one) - - but often hair dryer's are SO terrifying for cats, which is the last thing the sweetie needs. I also use Petkin Bamboo Eco Pet Wipes on ours when need be - - they're very gentle (and even Walmart carries them). They're like a baby wipe - not super wet, so he won't chill. I even warm them slightly in the microwave on SUPER low particularly if I'm using them on kittens.
And most of all - trust your senses. If he doesn't seem better, or even seems worse, and you just have "that feeling" -- get him in somewhere. I've learned to trust my "spidey senses" on this kind of stuff. So I hope he feels better - I'm so glad he has you to care for him (and care for his world in general in that he won't be making babies - - -or fighting for territory/females/all the "good stuff" that comes with unneutered male kitties!) and love him and make sure he's ok. So few people are willing to go through that much love, care and effort for what they'd call "just a stray cat." Obviously he's more than that to you -- - and it looks like the feeling's vice versa
Keep us posted!
