You can try a free online application which is capable of recording the activity happening on your screen of course including your Skype calls. Before recording, remember preset the audio input in case there’s no voice recorded. You can check here to see how to use it to record Skype calls.
"I have been looking to find a way to record my Skype VoIP calls. I do most of my interviews using Skype because my AT&T reception is very bad, I have to sit in my balcony in the northwest corner. I often lean over the balcony to get better reception. After almost dropping my phone and also myself off the balcony I now just make calls by Skype. The calls are recorded using the iPhone recording app carefully positioned closely to my laptop speakers. I still have no idea why Skype doesn’t implement this functionality.
Until that happens it’s time for me to branch out and find a better way to record my VoIP calls. In my search I came up with 5 great apps to record VoIP calls."