Yep - another vote for a full sine wave converter. ALSO, look on the label on the back/bottom of the CPAP to find out the watts/amps it draws (watts = volts x amps). Info should also be in the full manual. Get an inverter at least 25% bigger than the CPAP needs. Also get a remote on/off switch for the inverter if you plan on mounting it somewhere harder to get to - inverters draw some power all the time they are on. Keep your 12v wires as thick and as short as you possibly can. It's OK to then run an extension cord from the 120v side to your CPAP.
I mounted my inverter in the baggage compartment, right next to the battery compartment. Then have a long extension cord snaked up into the TV area (which is primarily what we got it for). But the cord is long enough to get to the bedroom for my CPAP.
Haven't dry camped for long periods, but over 3 days, it didn't seem to shorten the battery life significantly from what I was getting before.