I had my surgery on February 27th. I am an asthmatic, and had the surgery in hopes of improving uncontrolled asthma. I had a lung infection before surgery that wasn't resolved after surgery. I coughed like you wouldn't believe after surgery. In addition, I was on prednosone, which makes tissue more fragile (My surgeon put extra stitches into my hernia repair, because the tissue was so fragile he was afraid it wouldn't hold).
After my lung infection cleared, I had about 4 weeks of perfect lungs (the surgery did help my asthma), and then got the flu. Once again I was coughing constantly.
I coughed so much that my incisions killed--especially the one on my left rib.
After the flu resolved, I was into the tree pollen and allergy season. Coughing again...another round of prednosone and antibiotics.
What this all means is that if I can cough my guts out from the day after surgery, and intermittently until about two weeks ago (my lungs have improved, and I'm not coughing much again), I don't think you really have to worry about having a cough. It won't be fun, and your incisions will hurt. If you can avoid it, great, but don't lose any sleep over it.
While in the long run, I worry about the security of my hernia repair, (as an asthmatic, I'll cough more than the average post-Nissen patient throughout the lifetime of my wrap), my wrap has continued to work just fine, and my healing has continued.
So...don't worry! Your wrap will be just fine.
Take care and stay healthy !