Doesn't even need to be a CPAP. I had a sleep study done and it said I basically only had sleep apnea when lying on my back, and my doctor suggested a dental appliance to pull my lower jaw forward.

I got one from my dentist for way too much money, it broke, so instead I got a "snore reducing mouthpiece" from ZQuiet or SnoreRX which is basically the exact same thing but they haven't done a clinical study to show it reduces sleep apnea. I wear one every night along with a nose strip (like Breathe Right, but a different brand that I like better) and my mornings feel like I was hung over are long gone.