1. Run and set up a web server on your PC.
2. Use a special service for the domain for case of dynamic ip.
3.Give a link to the user of Skype.
4.Then s/he will open the link, the browser will run
Flash/Java/Ajax/HTML5-based Ekiga-like software.
5.Now you can chatting!
There are difficult
Or give him link to IRC webchat: problem solved.
Really, there are milions of chat solutions out there (web based or not).
I think you are not understood all might of the idea.
When I says Now, you can chatting!, I mean audio and video chat. Plus text
chat and file sharing.
There are many people who are forced to use Skype because their interlocutors
can not / do not want to install the SIP client. But we can