Why trust the injured man? Maybe he is not telling the trues. If investigations can not find the murderer(s), this file remains unsolved and nobody should be punished without having evidence.
Do not trust! Verify!
Discussion
How many more peoples have to die to you take a action?
Again, why trusting someone and killing other people without proof of guilty?
I think i got your point. In your story it is verfied that 3 of 4 shoemakers are the murderers! Right? The problem is only to separate the innocent one.. Well in this case i would isolate(imprison) all 4 from the rest of the city until time comes up with a solution to find the innocent one.