first, I think you should immediately stop communicating with that user, and end all connections with them. Delete and block them in your social media accounts and other avenues that have been used to communicate with them.
Then you can report them to email@example.com, so Skype can check and investigate their account and possibly suspicious activities. I think they can do actions against their accounts such as suspending them or making them ineligible to use Skype services.
However, it seems that Skype is only limited doing actions against their Skype accounts. So if you feel still necessary, you can also consider reporting this matter to your local police. Then your local police can contact Skype (most likely they already know how) to request for information or assistance that may possibly help them in their investigations.