WASAPI driver, Loopback mode
Before enabling set up a stereo track with record arm but DISABLE input monitoring, whether you have headphones on or not. The feedback is purely digital. Hence the CAUTION next to the mode.
Some people tend to record and co-host in Reaper, and then record the Skype call in Audacity. But I have found a workable way that you can record all through Reaper: setting up ASIO4All to include the Skype output.