The barber of the short story, "Just Lather, That's All," could certainly be considered more cowardly than the captain who comes to sit in his chair. Although the barber's secret affiliation was important to him as well the rebels, he could have solved many of his group's problems by using the blade to cut the captain's throat. His actions were not totally to hide his secret. He admits

But what would I do with the body? Where would I hide it? I would have to flee, leaving all I have behind, and take refuge far away, far, far away. But they would follow until they found me. 

So, the barber was worrying about his own safety and livelihood as well. His predicament left him in a situation where he could be called cowardly for either killing the captain or allowing him to leave.

I can't get you six paragraphs, but you could write quite a lot about the dilemma that the barber faces.  As a revolutionary, the general lying under his knife presents quite an opportunity, one that would bring him great glory in the movement if he were to take advantage of it and spill his blood.  It wouldn't take much, just a little extra pressure with the blade...

But it also presents a moral dilemma for him.  If he murders the general, what then seperates him from the monster that he believes the general to be?  Is there any honor to be found in killing a man in cold blood (essentially) while he sits defenseless in front of you?

Of course the admission on the part of the general that he came to see if he would actually be capable of committing murder puts the barber back into the cowardly light perhaps, but may also just serve to emphasize the difference between the general and the barber.

I'm sorry, but we are supposed to keep our answers around 90 words on this site...

I would suggest that you focus on asking what it means to be a cowards.  In my opinion, cowardice is knowing what you should do and then declining to do it.

By contrast, I think that what is happening in this story is that the barber is not sure what is the right thing to do.  If he kills the captain, he gets revenge.  However, by doing so, he will surely cause many more people in the village to die.

To me, he refuses to kill the captain because he does not think that this would be a net benefit to the village.