Tourist to Student application with criminal record

My husband has a criminal record in the United States from charges against him over 19 years ago, but no convictions. We want to visit China in March and then return as long-term students in June. The application asks if we have a criminal record in China or any other country. Since all the charges were either dropped or deemed adjudication withheld, should we just mark the box No? Our concern is that later when we apply for temporary residency as students, the PSB will do a more detailed background check and see the rap sheet that may contradict our application. We want to be up front and honest, so would it be best to just mark yes to the question on the Visa application and offer a detailed explanation now, or because there were no actual convictions, we are being honest by saying no on the application?