To clarify, there is not a version of SketchUp which will run from a USB device. You must have SketchUp installed on the local computer you’re using, which will then have the necessary paths and registry entries for the software to run. Even the latest version of Make will not meet this need.
In all likelihood this isn’t a feature which we’ll ever address as SketchUp is very resource dependent and jumping from a computer with an integrated, non-accelerated video card to a different computer with a high end video card is going to radically change how the software operates. We need to know all of that stuff up front to offer the best experience.