I think they are going to take cues from Smallville, Birthright, All Star Superman and Superman: Earth One. I think Lois will help, the glasses will help in masking a different look, they will probably add more than just glasses and thus have Clark create a "role" for Metropolis Clark, and Clark will have them because, even though Superman defeats Zod, the world on aliens is mixed, so Clark does all this in the first place so he can "hide" and yet be seen and still have a life while sorting his "Superman business" with the people, the government, and the world at large.
Also, even if Cavill as Clark isn't as much different than him as Superman, the best realistic way to explain it to audiences is still simple: people like me, you, anyone, has a "twin" because they look similar. Maybe they could pass off as your brother/sister or cousin from the POV of a stranger, even a friend. If someone brings up that Clark, from the DP staff, even Lois if that's how they go for her character, looks like Superman, but obviously isn't, and Clark now must have to "face that" for now on because people will think he is Superman, like a real life thing, people will buy that with no question. I think.