Skypeâ„¢ portable app made with Lightdesk. A telecommunications application software product that specializes in providing video chat and voice calls.
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Download and install the latest portable setup where you want then run skype-portable.exe.
If you have already installed Skype™ from the original setup, move the following files :

%APPDATA%\Microsoft\Skype for Desktop\* to data

Then run skype-portable.exe and remove Skype™ from your computer.
Upgrade
For an upgrade, simply download and install the latest portable setup.   
Modifications
Here is what differs from the original release to ensure portability :

Following switches are passed to the process.

–data-path=<data_path> : Directory where user profile is stored. <data_path> is dynamically generated at launch.

A shortcut is created at launch to allow native notifications and removed when Skype™ is closed
Data collector on RtcPalVideoEtwSession is stopped when Skype™ is closed

Configuration
Skype™ portable can be configured through the main YAML configuration file :

app:
cleanup: true

cleanup : Cleanup leftover folders (default false)