If you indeed mouth-breathe while asleep, it might be worthwhile for your doctor to investigate the reason for that preference; for example, a nasal obstruction that might be surgically relieved. Then perhaps, the use of a nasal cannula might be feasible.
If you are normally able to breathe through your nose but cannot while asleep, you might want to give consideration to the type of soft-gel mask commonly used with Nasal C-PAP. Oxygen can be fed into that type of system, at high concentration.
Finally if you persist with the use of a mask that enables mouth breathing your best bet would be consultation with an experienced respiratory therapist at a major medical supplier of respiratory equipment for a hands on trial of a variety of masks, to hopefully find one that has the best apparatus to secure it to your face.
Good luck
For the past 4 years I use a chin strap to keep my mouth shut and my mask interface is simply nasal pillows held in place by a head harnes -- the Oxygen tubing plugs right into the CPAP hose (need an adapter)
Talk to your CPAP supplier.
If you are breathing through your mouth that means your nose is plugged. I also have COPD and handled the problem by using nebulized acetylcysteine. That breaks up the mucus. Also, because of the albuterol and Duoneb that you might be using with an inhaler or nebulizer, this causes thrush, a fungal ailment, that starts in the mouth but can extend to the sinuses and lungs. Stay away from sugar, bread, and carbohydrates in general. These are foods for fungus that causes mucus.