I have a CPAP (i snore like no one's business and have the most enormous tonsils you've ever seen!) and I've travelled all over the world with it, you can just use a normal travel adapt to change the plug type like a hairdryer.
The current machine I have has got a US plug for mine as it's a US machine(purchased over the internet as my NHS one was a bit rubbish and I wanted something more up to date) , and I have it plugged into a normal travel adaptor in my bedroom and have had it there for about 18 months.
My other one is a UK one (my NHS one) and has been all over Europe, Texas and the Far East (for 6 weeks) on a worldwide adaptor
I've never had any problems with customs, but...you should get your gran to get a letter from her doctor just in case. I normally keep the hoses in a seperate zip lock bag from the machine, they scan the machine and leave the hoses/mask in the bag so customs don't touch it.