No. Lycanthropy (werewolf transformation) is exclusive to the base Oblivion game via the “The Witch’s Curse” questline (Hircine’s Daedric quest). The Shivering Isles DLC does not include this mechanic.
If you want to be a werewolf, complete Hircine’s quest in Cyrodiil before entering the Isles. The transformation works in SI if already contracted, but you cannot become one there.