why not simply install the software in both OS in a natural way? You can always configure your download files and whatever config files to be in the same place, say in E: in your example. But having two copies of the executable in your system you will not waste too much space, right?
Otherwise Jonathan's right - the registry entries should be there in both OS, unless you are dealing with a self-contained executable that does not need to be installed and can be run from whatever location. I have several programs like this, emacs most notably, but whether there are any download managers of that sort, I am not sure.