Will I be sinful for lying and exposing a Muslim woman by saying that the child is not the son of my brother's wife, and by telling my friends that we found him in the street, even though my intention was not to expose her?

Your statement that the child is not the son of that woman does not constitute slander. However, your statement that your brother found him in the street is a lie and is not permissible unless it serves a greater good, such as concealing the faults of your brother and the woman. The majority of scholars hold that this child is not attributed to your brother's lineage, though some scholars believe in attributing the child to the fornicator if the woman was not legally married to another man and no one disputed the lineage, as held by Ishaq. As for his lineage to his mother, it is established in all cases.