Why would you think he will have to be put to sleep if he has a collapsed trachea? There are many treatments from cough suppressants to brochodilators to weight loss that can help. Switching from a collar to a harness, not exposing him to cigarette smoke, etc. also can help. In most cases it can be managed medically.
The first step is to take him to your vet and have him examined.
Tracheal Collapse - VeterinaryPartner.com - a VIN company! Collapsed Trachea in Dogs