If you try to verify your Skype account for sending SMS messages, but you don’t get a verification code via SMS.
The cause could be that you a already added your phone number to CallerID option.
What you need to do is, to log in into your skype account and delete CallerID number, then ask for SMS to be sent again.
This should work immediately, and when you verify your number for SMS sending, you can ask for CallerID setting again.