After much research I have found there is a lot of incorrect information, both on the forum and outside of it, regarding bringing a CPAP machine into Japan.
You must apply for a Yakkan Shoumei. I am sure many people haven't, and perhaps have travelled many times without it, but the correct proceedure is to apply for one.
Below are two links. The first with information regarding CPAP and other medicines and the second is the actual application form with very easy to follow samples provided. (Also included in the links is the email address to send a query to regarding bringing other medications with you.)
I sent my first email to the Pharmaceutical Inspector to check if I also had to apply on my Yakkan Shoumei for any medication I take and I included my CPAP machine in the query (I was still sceptical about needing a permit for it). I received a reply within two days and the medication was fine but an application was needed for the CPAP. I completed the application, using the sample on the above link as a guide, I included a letter from my doctor and a copy of our airline tickets. I received my Yakkan Shoumei the next day via email.
I have also applied to the airline to use the CPAP machine, another simple process.
You can send a query to the Pharmaceutical Inspector any time but applications must be submitted within 6 months of travel and no changes are permitted once received.
I hope some of this information is helpful to someone. Yes, it did take a little time to complete the paperwork, but that is all sorted now and ready for our trip and I know the correct proceedure has been followed. Thanks.