In "Just Lather, That's All," the barber is very skilled at his profession and takes great pride in his work. This is shown by his preparation of the razor and shaving soap at the beginning of the story and also by his "careful" approach, ensuring that the Captain's "tufts of hair" do not cause the razor to go "astray" and make the Captain bleed.
Secondly, the barber knows the difference between right and wrong. Specifically, he knows that murdering a person creates as many problems as it solves. This is shown by the following line:
No one deserves to have someone else make the sacrifice of becoming a murderer.
In addition, the barber also realizes that if he kills the Captain, it will only lead to more murders because people will want to avenge the Captain's death.
Thirdly, the barber is not spontaneous. He likes to have a solid plan in place before doing anything. When he thinks about killing the Captain, for instance, he also thinks about where he would hide the body and where he would go to avoid capture. This characteristic is also shown by the very fact of his dilemma. If he were spontaneous, he would kill the Captain without a second thought. But the fact that he does not do this shows that he needs the reassurance of planning and preparation.