SIGIL is probably not your best tool for creating static HTML files although it's not impossible.
The main goal of sigil is to produce an epub file, and to read an epub in the browser, you'd need to install a special extension (Readium).
If you get down to it, epubs solve a navigation problem -- of flipping between chapters and of creating a TOC.
On the other hand, an epub is just a zip of html files and some extra navigation stuff. I build my epub files in another way (Docbook XML --> static HTML --> EPUB) -- but when testing/editing, I view each chapter and the table of contents web page in a browser.
I don't know if Sigil has a button to turn your files into an epub file, but my guess is that at some point, the chapters and TOC exist as HTML files. Even if they don't, you could simply rename the .epub to .zip and then unzip.
The file tree for epubs are fairly standard; here's what's generally inside.
You could just ftp the oepbs directory to your website and you'd have all the static pages there (you might need to rename the toc.html to index.html so that's the default view. An index file in ebook usually doesn't refer to the TOC but the subject index at the end of the book.
So SIGIL could probably get the job done (and is especially recommended if you are using internal links between web pages), but a simple html editor would work just as well. (Heck, even MS Word to HTML could do the job, although you'd have to live with ugly code).