I've created a version of Bricx Command Center that works on your USB flash drive and leaves no registry entries or data behind (other then what was there before). It fully integrates with the PortableApps.com Platform, which is recommended but not necessary.
You can download it below:
Download Bricx Command Center Portable, Development Test 1
This is only a development test, so please report any problems you are having with it.
Tip: This includes a full installation of BricxCC. You can copy a custom installation of BricxCC into the App folder - remove the already present