If a program runs without installation (just unpacking it to a separate folder allows you to run it sans problems), then there is no issue with registry. Otherwise, you'll have to make a registry snapshot before you run the install, then another right after that, and compare the two. I cannot quote the snapshot-making program names off the top of my head, but they exist in great numbers (and some of them are free). Try at Winternals / Sysinternals, that's always a good place to start.
Or you can do it the hard way, install things on the external HD anyway, then unplug it, carry it bodily to another box, and try running the app in question from there. If it runs, then you know that it either does not make changes to the registry, or even if it does, it doesn't really need them. If it doesn't run... tough.
If you go for the "install anyway" option, I'd suggest doing it on a test box. A word to the wise: even your usual computer can make a test box in a pinch if you have disk imaging software (Acronis True Image, Symantec Ghost...).
Now, for the installation on other laptops: everything depends on those registry changes. If a program runs without being installed first, then all you have to do is copy the program's folder to the target box and voila, you're set.
Hope this helps :-)