I think in either case, you will be symptomatic if you are going to get into a problem underwater. If you have recovered from a cold to the point where you are no longer coughing, the likelihood that you have significant pulmonary obstruction is very low. (The exception is in the elderly, who can have horrible pulmonary infections with no symptoms -- but I don't think there are many debilitated, frail 80 year olds diving.)
If you have significant coughing, whether it's producing sputum or dry, it's worrisome for some bronchospasm. Many persistent, dry coughs after viral illnesses are due to this. At the absolute least, I'd get an exam by a physician before diving with a significant cough.
If you have significant coughing, whether it's producing sputum or dry, it's worrisome for some bronchospasm. Many persistent, dry coughs after viral illnesses are due to this. At the absolute least, I'd get an exam by a physician before diving with a significant cough.