Two possibilities here. 1.) He is delusional or 2.) He is rational and has some basis for believing that wifi causes him headaches.
Explanation (1) has been popularized by television show Better Call Saul and can't be dismissed, it is possible that the ritual of checking a room and finding an acceptable one makes him feel psychologically better so that he does not get a headache.
I have seen enough strange things in my time that I would allow him the benefit of the doubt (2) that wifi really does impact him, that is, if no other unusual behavior is on display. Some people seem highly sensitive to ordinary things that don't bother the rest of us. Some sensitivities may be extremely rare too.