A CPAP doesnt mean you have to have an inverter.
Many actually run on 12 volt DC the same as your battery system in most RV's. If your unit has a plastic block (Like a brick) in the power cord there is a good chance its a converter to give the machine 12 volt dc power.
Check your unit, verify brand and model number and then go to either the manufacturer or to an aftermarket seller to look for DC power cords.
Here is one site that sells these products, there are many others.
CPAP The round cigarette lighter style plugs are usually found somewhere near the bed, so hopefully you wont have to install one.
My unit without the humidifier uses about 4 amps when running, m'ladies with humidifier uses about 7.5, so you may want to increase the size of your house battery.