Could you somehow scrape all users and get an IP address -> skype name mapping? You could then know the Skype usernames of all visitors to your website.
No this not possible. Only skypename -> IP, and only email -> skypename. You can parse whole skype network and store all IP's if you can handle so many data.
The geek part of me wants to do this / see this done, the part of me that oversees a few popular content sites thinks there isn't a huge amount of benefit to it. Even for malicious purposes, Skype is a very poor option for spamming.