My own personal ideas about this question are that we have no reason to doubt the barber--I do not think he is presented as a narrator that is in any way unreliable, in that we are given no reason to think he is deceiving either us or himself. Certainly I can see why you might think he is, to excuse his cowardice in not wanting to kill Captain Torres. However, I think at the end of this excellent story what the barber experiences is not cowardice but a kind of epiphany or insight into his position in the world and that of Captain Torres. Note what he says:
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.
It is this central realisation, that every person has his or her own place in the "scheme of things" that gives this monologue a note of authenticity. The barber recognises that he is a barber and that he does his job well. Likewise he comes to understand that Captain Torres has his own place in the scheme of things - he does his job well too. Therefore I think the barber comes to gain a kind of grudging respect for Captain Torres, which I think we can say that Captain Torres shares by the end of the story.