Microsoft is moving toward making good on its promise to ultimately allow Skype to work plug-in-free.
On April 15, Microsoft announced Skype for Web, Outlook.com, Office Online and OneDrive now can do voice, video and group video calling without plug-ins when used with Windows 10’s Edge browser.
The first supported plug-in-free Skype scenarios include:
Read this

Microsoft makes Skype for Outlook.com globally available
Microsoft also has fixed a Skype call-ringing-after-pickup issue with a new plug-in enabling Skype integration with Outlook.com, officials say.
Read More
Microsoft is still committed to providing plug-in-free Skype support on other browsers, officials reiterated in today’s blog post.
“We will continue to work on enabling audio and video interoperability with Chrome and Firefox browsers, once they both support the H.264 video codec,” the post said.
The new Skype plug-in-free functionality is considered to be in preview at this point. It’s enabled on Edge on Windows 10 Build 10.0.10586 (November update) and above. As Microsoft cautions, “some features like Screen sharing and Calling landlines and mobiles require you to install a plugin.” Also: Users may be prompted to install a plug-in if the remote participant isn’t using the latest version of Skype for desktop or mobile.