I've had the same question in my head for a while. A while back I purchased some 2mb Sandisk USB memory sticks. The interesting thing is that there is a tiny operating system on each stick...I think it is called "U3"...or something like that. Anyway, I haven't tried it yet, but I'm thinking that if I can install that U3 software on my external hard drives, I might then be able to literally install CCleaner onto that external drive and run the program that way.
Like I said, I haven't tried it myself, but there HAS to be a way to either point it to the external drive or run it from the external