CPAP is the first line treatment for this condition with surgery reserved for patients for who CPAP does not work or who refuse to use it. In your case, your cardiomyopathy (and history of dangerous arrythmia during sedation with what was probably propofol -- though you should check to find out for sure) makes you higher than normal risk for surgery of any sort so CPAP would be a safer option. But if preferred there is no harm (other than possibly wasting money) in first trying oral device (s), there are actually 2 types that can be tried, one pushes your lower jaw forward, the other holds your tongue forward. Both would need to be fitted by a dentist or oral surgeon specializing in same. If dead set on having surgery, there is something called a sleep endoscopy wherein they can directly see what your upper airway is doing when you are asleep (it is done with IV sedation), and that helps in pinpointing the mechanism of the obstruction (which can vary and often involves more than one thing) , however there will be some risk to you in even that given your history, and it would be important to have tell doctor and anesthetist about your history. Most anesthetic agents reduce myocardial output and that is dangerous in someone with your cardiac problems. Are you at all overweight? As if so, losing weight usually helps this condition.
