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.