When I was on the CVN-69 a couple of years ago, the guy in the rack underneath mine had sleep apnea. He had a machine that he slept with every night.
I'd be very surprised if if the CVN-70 has any legitimate "rack-tricity", although your son might be able to fix you up in a rack that does have it (which by the end of a deployment there are bound to be several racks that have been wired). If not, he could probably get an extension cord from the electricians on board which could be plugged into the legitimate stanchion mounted outlets.
Like 93-383 said, have your son ask his chain of command about accommodations. They will certainly be able to work with you guys about this issue, as many of the sailors on board probably have the same condition. Enjoy your "cruise"!