There's no way to use Skype via a browser or anything like that. But if you can use a USB thumbdrive you may be able to use a "portable" install on a thumbdrive. See this link for directions:
13-05-2012 16:14 - edited 13-05-2012 17:26
Imo.im is a website that allows you to use Skype along with other instant messaging programs such as MSN, Facebook, Gtalk etc.
that may be ok if all you wish to do is IM, but Skype provides so much more than instant messaging