It is not completely clear to me what you are asking…. It seems Skype offers this integration with any number on the web, as long as you have some Skype-out credits. It is much more common to have live “chat” (IM) for customer service on the web.
You may be asking about a kind of Intercom system for your website, using Google Web Speech API. The drawback here is that the Web Speech API is limited to the Google Chrome browser, I believe. Also, as far as I know, the Web Speech API is still undocumented. In any case, I am not aware of any CRM system employing this technique to date.
You may wish to refer to my quick and dirty webpage: