This is an interesting question to consider in relation to this story, because actually, although the barber works hard to keep his inner feelings from being noticed by Captain Torres by trying to present a smooth exterior, the ending of the story puts into question how successful he has been, as we find out that Captain Torres has known about the barber's rebel sympathies all along.
However, if you are looking for quotes to support your theme of appearance vs. reality focusing on the barber, the first paragraph would be a good place to start:
When I recognised him I started to tremble. But he didn't notice. Hoping to conceal my emotion, I continued sharpening the razor. I tested it on the meat of my thumb, and then held it up to the light.
Here we see the barber's own direct reference to appearance vs. reality as he talks about concealing his emotions. Later on the barber says that "he was upset" as he continues in his task, and clearly the words that he says in his conversation with Captain Torres, when he agrees that the "fine show" was "very good" are another example you could refer to. Look for other references to his hands trembling and his internal thoughts as outwardly he does the job of an excellent barber. Hopefully these ideas will get you started. Good luck!