As several members pointed out here. Saying to me or to any other person who is not Orthodox, that we should accept the Book of Wisdom just because the Orthodox Church says so, is not an answer. It is harmful more than it is good, because it may be seen as lack of answer. It is like saying because the Bible says so. That doesn't explain that much or answer any question except for someone who is Christian and holds the Bible as the highest authority. It is like saying, God doesn't exist because Richard Dawkins say so.
So far, I didn't get a very clear Orthodox answer to the question, Is it a sin to not believe that the book of wisdom is inspired ? In the Catholic Church I think it is sinful, because the Catholic Church clearly says that the book of wisdom is inspired. In Orthodoxy however, there are several types of Bibles for several Churches. For example, the Ethiopian Orthodox Church is believed to have the largest Bible, even books that do not exist in the Septuagint. Does that mean the rest of Orthodox Christian are committing a sin by denying the these books are inspired ? I don't think so. Is it a requirement to believe that God inspired the second canonical books are fully inspired by God ?