You can get married without witnesses in Indiana. Witnesses are not required to be legally married in Indiana. There is no place for witnesses to sign on the actual marriage license. You can "kind of" get married in secret.
A marriage license is a public record. Many newspapers publish the marriage licenses they issue in the newspaper. The Indy Star does not publish marriage licenses issued in Marion County. Other counties in Indiana do.
If someone knows how to search government databases, they can find your marriage.