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 drive directly.
I'm not too familiar with the technology behind the U3 program on the Sandisk drives, but perhaps there are other freeware programs similar to it that can be downloaded and installed right onto your external drive.
I know it goes w/out saying that I wouldn't go experimenting on the external drive that contains all of your critical data/files. Do you have another drive you can test this on?
I know this isn't much of an answer, but you got me thinking again about the possibilities here. I think I'll try downloading CCleaner onto one of these Sandisk drives and also try to install it there as well. Once I run it from the USB drive, perhaps it will give me other options or allow me to point the cleaner at an external drive. If not, I'll download and try to install CCleaner onto another external HD that I have. If that doesn't work, I'll go search for the U3 program from Sandisks website (or find something that is equivalent from download.com, pcworld.com or majorgeek.com) install that onto the external drive (I may have to partition it first) then download and install CCleaner onto the external HD that now has the U3 or equivalent small OS on it.
My apologies if that is as clear as mud...but I'm trying to think it all the way through before I've even attempted it.
Lets stay in touch on this topic.