What ports do you have your web proxy set up to. Is it just the standard ones as installed or have you edited any of them?
Here is what my standard set covers:-
These ports cover all the ones used by Skype.
I certainly have Skype working with my web proxy enabled.
Could you show the settings in your web proxy page?
Do you have the logging enabled in it. If yes then you maybe you can see in the logs what is happening when you try and access Skype.