Wooly Bully by Sam the Sham and the Pharaohs is not a one-hit wonder according to the criteria of this list. The group also broke the Billboard Top 40 on the Hot 100 pop chart with Juju Hand (#9), L’il Red Riding Hood (#2), The Hair On My Chinny Chin Chin (#22), and How Do You Catch A Girl (#27).
No, I’m not going through and disputing all non-One Hit Wonders. As I skim the posts, I notice nominations for groups that I know also had additional Top 40 hits.