Specifically for Skype, there's Magic Camera under Skype Apps on their "extras" page.
Within the main features list, I've highlighted the relevant feature you're looking for:
- Languages: English, Arabic, Bulgarian, Chinese, ChineseSimplified, ChineseTraditional, Danish, French, German, Hungarian, Italian, Lithuanian, Norwegian, Polish, Portuguese, Romanian, Russian, Spanish
- Add pre-recorded video, photo albums, animations and desktop screens to your Skype calls.
- Record Skype video calls.
- Create amazing video effects with just one click.
- Funny photo frames and fantastic video transforming effects available.
- Face tracking and mask effects available.
- Type or paint pictures directly on your video calls.
- Webcam video overlay.
- Picture in picture.
- Real-time video backgrounds replacement.
- Free webcam effect packages available online.
- Make your webcam avaliable in multiple applications in the same time.
- New, easy to use design.
They have a free trial, and if it solves your issue, it costs $19.95.