This is sort of the same type of problem that I'm probably going to have soon. I just purchased a touring bicycle and I hope to eventually lose enough weight that I will be able to go on a five day, 300 mile, self-supported bike tour sometime this summer using a tent at various campgrounds at night (some with electricity, some without), then go on the
RAGBRAI (ride across Iowa) in the following year , and then do a 2-week, 1,000 mile self-supported trip after that.
I imagine that the weight loss will help my Sleep Apnea, but I'm not sure if it will go away completely, even when I get down to my target weight. Sure wish it would, though! <_< I'm at a pressure setting of 14 right now.
Like your Peru adventure, with loaded bike touring, overall equipment weight is a huge issue. Each extra pound you tote on a bike or pack in your backpack makes it harder to walk or pedal. So I might have to check out small, lightweight CPAPs for that purpose (but cost is also a factor), I may just end up carrying my existing Remstar Pro.
Fortunately for me, most of my touring will be in the U.S., where proper planning for electrical needs will pay off, since a lot of campgrounds offer electrical hookups. For remote areas in Peru, you won't have that luxury.