You don’t need to have any Facebook account in order to be able to use Skype. What is your problem?
If you have a skype account and a face book profile - and you try to register another skype acount ... the skype site asks you to do it using your face book account details ,,, !!! so how do you register without face book ?????
for my opinion maybe u register your skype account using fb connect .
you can register another skype account not using fb connect