You didn't specify what type of design work you're doing or what platform you're working on.
If you're working on Windows machines, there's a decent amount of PortableApps that might suit your needs such as Gimp, Inkscape & Blender (3D). Modern browsers like Chrome and Firefox have powerful built-in features for web development and can be extended further with plugins and extensions. The PortableApps.com platform is a complete app management solution that allows for portable fonts as well. There are other portable applications sites around if you do some web searches, but imho they have less oversight and "polish".
If you're able to boot from the external drive, you could install a linux distro to the drive and have a portable OS with these apps and more. So long as you don't install proprietary graphics drivers, you should be able to use the OS on multiple PCs.