You might find this article interesting:
Symbol font – Unicode alternatives for Greek and special characters in HTML
http://www.alanwood.net/demos/symbol.html

It does not, however, explain how to modify your Word document so that any symbols it contains are replaced with their Unicode text font equivalent.

Symbols inserted into a Word document through Word's Symbol Dialog Box should display correctely in all browsers when saved as web pages using the SaveAs dialog box. This is not the case for symbols inserted into a Word document by changing the font to a non-text symbol font (this is probably why you are having a problem).