"Skype for Web" requires a proprietary Skype Web plugin (available only for Mac and Windows). This can be avoided.

On Chromium use this add-on, and select "Microsoft Edge 12".

On Firefox use this add-on and set your user agent to "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/46.0.2486.0 Safari/537.36 Edge/14.14295". -- But for some reason Firefox makes Skype say 'Call ended' immediately after allowing microphone access. Chromium is recommended instead.