There is a tape called somnifix that you can use across your mouth. I use 3M 'strong hold' water resistant tape, blue in colour, comes in a 4 yard spool.

My first night on CPAP was marred heavily by my lips going slack and air coming out. I called my RT and she suggested chin strap (Nope, I told myself instantly...) or that some tape their lips, which she couldn't recommend. Well, I have taped ever since Night the Second on CPAP and have not looked back. A great many CPAP users must tape or they simply don't get the therapy.

Look, you can get used to anything if it's important enough. And that's the bottom line here. Nobody wants to have apnea, and nobody wants to wear a mask and elephantine hose at night. But if it means 15 more years of showers, meals, hobbies, family gatherings....what's the big problem?