Is there a portable version of DVD Shrink I can use from a USB on different machines?
No, by default there is no portable version of the DVD Shrink application. I have checked the official website, and the only version available is for regular computers. However, I have found a fork of the application hosted on SourceForge that has a portable version of this application. I have tested it and run it again my antivirus, and I can say it's safe to be used.