The experience of flight is wonderful; it is the thought that is bad --- the fact of mere air holding up a 100000lb+ aircraft is unthinkable it is that simple. Having experience with aircraft engineers only makes matters worse.
As for surgery this is another matter. I always flew with my WPW, but mine only setoff when I was exercising intensely. Nevertheless, surgery for WPW takes several flavors beyond simple ablation, wherein complication rates can drive prudent thinking. In this case, if a person is currently in a position of relative safety, I can certainly understand postponement.
I am a million miler myself, and suffer from AFib which was controlled well in the past.
Flying lowers the pressure one is breathing and so makes for less oxygen available - so I would say anyone for any reason who suffers from a shortness of breath would find that worse at altitude. But as they are sitting still it most likely would not be noticed.
Others are breathless when flying for reasons that have nothing to do with cardiovascular health - had some fear of flying myself and being an engineer have some doubt about engineers - sad to say.
I've a number of transcontinental along with many eastern seaboard hops and never experienced any difficulties. I know of no reason that an electrophysiology study would be postponed on numerous occasions unless cancelled by the patient themselves. You have to go in there with a positive attitude. Is it possible this person is not mentally prepared yet?