There are plenty of extensions that will let you change the UA for any site; having yet another one with such a narrow function seems to me like those "we have a smartphone app too" whose only purpose is to open the browser to their site.
But if it's your only use of such a thing, as it is for me, it's just one click away. You can also feel reasonably safe as the extension works only on Skype's web sites per Web Extension manifest.