I took a look around the Skype forums and I found this question posted there as well. Here's the post link if you want to see all of the responses:
Can you integrate Skype into website?
The answer is basically "no" per Skype. You can embed links and as long as the client has a Skype account it will jump to the Skype application. You cannot embed the Skype window within the Website, though.
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