You may want to try FiddlerCap, which is a light-weight version of Fiddler (using FiddlerCore) in the sense that it captures traffic and saves it to a Fiddler archive. It does require an install by default, but you can avoid that if you:
Install the FiddlerCap download on a different machine first. This basically does an extract only. You can simply distribute the files to the intended target machine.
Add the FiddlerCap folder on the target machine to the PATH environment variable, because it needs to find FiddlerCore.dll in that folder.