This excellent tale of suspense and tension naturally gives rise to a number of thesis statements. To me, the most natural and obvious one to focus on is examining the character of the barber in this short story and the decision he has to make of whether or not to kill Captain Torres, who has sat himself down in front of him for a shave. It would be the easiest thing in the world for the barber to lean over and slice his throat open with his razor, and yet he does not. Thus your thesis statement would be "The barber makes the right decision by not killing Captain Torres."
To examine this further you would want to examine two aspects of the character of the barber, focussing on his dedication to his job and also his view on violence and murder. A key passage you will want to talk about comes towards the end of the story, when we increasingly read a kind of stream of consciousness narration as we hear the internal thoughts of the barber talking through his options and motivations in his head:
Murder or hero? My destiny depends on the edge of this blade. I can turn my hand a bit more, press a little harder on the razor, and sink it in. The skin would give way like silk, like rubber. There is nothing more tender than human skin and the blood is always there, ready to pour forth.
But I don't want to be a murderer. You came to me for a shave. And I perform my work honourably... I don't want blood on my hands. Just lather, that's all. You are an executioner and I am only a barber. Each person has his own place in the scheme of things.
These two paragraphs in a sense capture the essence of the story - the narrator comes to a point where he almost has a grudging respect for Captain Torres - for his place in the scheme of things, as he realises who he is not - for he is not a murderer, he is a barber who takes great pride in doing his job well. The acknowledgement of Torres at the end can also be seen as a grudging respect in turn, for Torres realises the chance the barber had and the danger he was in. Hope this helps and good luck!