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you should look in the preferences there should be something mirror webcam or not.
 
I think that Skype only reverses the video on your computer so during a video chat you will have a mirrored picture of yourself but the person you are talking to receives the video the correct way round. You could check this easily during a video chat by holding up some writing as you have mentioned.

If this is not the case and the person you are talking to also receives mirrored video you could use a application like iGlasses. I'm pretty sure that it lets you mirror your video.
 
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