Excellent idea, what is the space requierment again for Tiger, as I do have a 2GB flashdrive laying around....
Standard fresh install is around 5 GB, then you need some space for swapping (say 2 GB), so the 7,4GB of the black nano are a good start.
2GB won't get you far, you need some free space to keep it fast enough. Use a USB hub, connect all your flash drives to it, and use OSX's disk utility (it's also on the OSX install disk, so you can do this when installing) to make a striped RAID. They've done a RAID 5 with the original Shuffle, which was kinda cool as a system drive.