You have to chat with a Skype representative to get the account deleted. You can't access the chat support unless you are signed into the account (thus no direct link).
If you can't find any contact info and still wish to ask something, for example a question about what exactly is deleted, about data retention, etc., you may contact the domain owners using this info.
If you signed up for Skype using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Skype. Click the icon below to find out how.