Should the sheriff and Atticus have hidden the fact of the white man’s death in light of the novel being a plea for social justice?

Are you referring to Bob Ewell's death? Race isn't so much an issue in Bob's death as Boo Radley, who killed him , is white. As for social justice, the truth about Boo Radley would have harmed Boo himself. Boo could not handle the attention and it was better for all involved that Bob "fell on his knife". This is a case of making the best out of a bad situation.

You call him BOB Nelson, not white man.