Perhaps I don't quite understand what you're asking with regard to the SHAPE of the character.
If I create a character and assign the shape of a bottle or cat, then save it as a Project file, the character will display as a bottle character or cat, etc.
I could send a friend that character with it's assigned shape and my friend could then open it in PP.
Actually when one saves a Project file in PP it's actually a working Haptar (change extension to .htr to use with Hal).
It's stored in the C:\Program Files\Haptek\PeoplePutty\user\figures folder as myProject_figure.haptar - the jpg's are just 3k thumbnails.
As far as saving a shape, I assume you want to save that shape of a character?