How do I feed Skype a prerecorded video?

Sure you can.

You can use the Webcam Studio, which will allow you to use pre-recorded media, such as images, audio/video, etc. as a source to create a virtual "bridge" between your live streams (webcam, digital cameras/players, etc.) and other media.

Unfortunately I don't have who to call in order to perform a test right now but I have used this for both Skype and Web Based Services like Ubiqq (http://www.ubiqq.com) and Ustream.TV (http://www.ustream.tv/) As shown in the provided screenshots.

On this screenshot you can see Skype recognizing Webcam studio Video Device (/dev/video0) as a source, somehow the "Test" button won't work (at least on my system) but it works when on a call.

This screenshot shows the usage of the Virtual Video Device from WebcamStudio on ubiqq. Which is a flash/web based video conferencing system.

Give this a try. Webcam Studio will allow you to choose both live and pre-recorded media, and enrich it with effects which includes animations, text, and further more.

I hope this help you and if so, enjoy!

Good luck!