I'd say that if the vet doesn't think it's a respiratory infection, then I wouldn't worry too much.
Having said that, it could be anything - cats commonly get things like blades of grass stuck up their nostrils, so that could be tickling him and he's sneezing/coughing/hacking to try and get rid of it... it could be polyps perhaps (not sure if cats suffer from it, but I guess it's possible) - kind of haemmorhoids but in the nasal cavity... maybe he possibly has trouble swallowing all his food when he is finished eating (if the noises happen after feeding), or something could be obstructing the airway when he gets excited or plays.
Like I said, could be anything! If it doesn't seem to bother him too much and he is pretty happy most of the time, and you don't want to or can't spend a lot on him, then I wouldn't be too concerned. Keep an eye on things though, as you never know what could happen. Obviously when you do rehome him, you will have to mention it to the new owners/caretakers.

Good luck with the rehoming, let us know what happens