Glad to hear that you had a good chat with the vet.
Jack's wheezing/hacking on walks -- is he really straining/pulling in the harness? If that is the case, you may want to consider a different style harness and working with him to stop pulling. I had a mesh harness that Maximo really strained against and I found that it was putting stress on his neck. I switched to the Buddy Belt because it doesn't come anywhere near the neck.
There are videos somewhere here on the site that demonstrates the differences between reverse sneezing and honking that is associated with CT. I'll look and post the links.
Hope Jack feels better soon.