Cancelling your Skype should not have to include cancelling all your other Microsoft services
you can do the following.
Change Skype mail for another.
and once the Skype is separated from the services of your Hotmail account
In your Hotmail account, if you re-enter Skype, an account will be generated with lots of random numbers. I recommend you change the name of Skype for another and Dad, I recommend deactivating that you can search in the search engine.