I don’t use Skype, but I am going to assume it is something that goes through your computer. Personally, if I need to capture the audio and video from my computer, I plug my nanoFlash to the HDMI output of my video card, configure the sound to go out via HDMI as well, and then just record it all to the nanoFlash.
If your sound card has a "What You Hear" or "Stereo Mix" channel on the recording mixer control, you can simply use that. I just called the Skype "Echo/Sound Test Service" and recorded it directly into Vegas. Worked fine.
Of course you can only record the other end of the conversation. If you want to record both sides of the conversation neither my method or the others already mentioned will do that because you'll have to re-route microphone input. You'll need to find a utility that works with your sound card which lets you route and mix the signals within your computer.