VideoPad is a professional fully blown video editor.
It's arguably the best completely free video editor currently available.
It is free for both personal as well as commercial use.
The installer itself is only 600 kb, however, during installation it downloads ffmpeg3.
When fully installed the total size is around 7 mb.
VideoPad has no dotnet, gtk or java depenencies.
It does store its settings in the following registry keys:
However, after installing VideoPad, copying the "C:\Program Files\NCH Software" folder to your usb stick is sufficient to have made it portable.
Simply run VideoPad\Videopad.exe to start it.