a wraith. The part when Fawful absorbs her essence before storing her soul into Bowser indicates this. She has no true body because it's actually a soul. The body takes her form as well, so for all we know, Cackletta may have possessed a Bean person and thus, gave her the form we recognize her as the most. Also, this is a Japanese trope.
In Ninja Gaiden, Doku's actual body is a samurai soul. He just inhabits a suit of armor at first.