This is a great question and one you may benefit from asking in the discussion postings of this group to gain a range of different views and responses. This clearly is the central issue that is raised in this excellent short story, and I think it is clear that the barber comes to the conclusion that violence is not justified - at least if he has to perform it. He comes to understand that Captain Torres is just a human like himself, trying to do his job to the best of his ability, and he also recognises that to commit a murder is not an easy feat to achieve.
I must admit, if I were in the same position as the barber, I would be unable to kill Captain Torres for the same reasons. I also think we have enough historical examples of political change being brought about peacefully - consider Gandhi in India or the Civil Rights movement in the States which were both successful because of the absence of violence in their campaigns. I look at these historical examples of successful non-violent political resistance and they give me hope that if I were unfortunate to live in a state where I felt I had to protest, I could do so effectively in a non-violent fashion.