Very little additional cleanup is required. All of the styles I use in Word are in the stylesheet (10 - 20, depending on the book). If I've done a good job assigning styles in Word there isn't any extra formatting. It is easy to delete all the Word style information in the header.
Word does style the normal paragraphs style=MsoNormal, which I do a search and replace make just a p element.
I do all of this while it is just one file in Sigil. Then split the file into chapters and it is pretty clean. Makes it easy to use Word's Table of Contents, Endnotes, and Bibliography.