Desktop is just another
X application that displays whatever it wants - it's a matter of history and tradition that mostly people just want icons there, although widgets have become quite common in the last 5 years. Unlike the mainstream desktop environments, more lightweight standalone window managers don't start a desktop application on their own, and mostly just set the color/image of the root window (the window that contains all other windows). Ideally you would want to stop the whatever application manages the desktop - then you are left with just a blank root window, and it doesn't mess up all your icon settings (which will probably happen if you just move the shortcuts somewhere else).
The desktop application may be
nautilus (gnome), and others. For each specific case, it depends on the DE wheather or not you can disable auto-restarting the desktop if it closes/crashes. If it doesn't interfere, you may be able to just kill the process. You may also be able to tell DE what to do via dbus (very case-specific).
It may be possible to have two desktop managers installed, in some cases, starting one replaces the other.
I realize this is not a complete answer, just a rough plan (too long to put in a comment). Feel free to comment on how to proceed in each particular case.