You have to get Chromium in an odd way. You can get it by executing the following:
sudo dpkg -i chromium-codecs-ffmpeg-extra_45.0.2454.85–0ubuntu0.15.04.1.1181_armhf.deb chromium-browser_45.0.2454.85–0ubuntu0.15.04.1.1181_armhf.deb
Then, go to your File Explorer and run each .deb file with Package Installer. This should install them to your system.
The reason I think this should work is because YouTube.com/TV, a HTML5 heavy webpage loads with a bit of lag while on Chromium. I would think that if it can load that page, it should be able to load web.skype.com.