In XFCE, I wan't able to drag a menu item from the applications menu onto the desktop per @Graeme's nifty trick. Grepping around, I found the application menu items are all defined in
/usr/share/applications/*.desktop . Grepping that dir for e.g.
Name[en_GB]=Screenshot (I suspect that the en_US is just the entry with no langtag:
Name=Screenshot), I found that
Exec=xfce4-screenshooter. Sure enough,
/bin/xfce4-screenshooter was in my path and strongly resembled what I got when I clicked the button.
Voila, a solution at one point in time for one window manager, but the dir
/usr/share/applications/ gives me some hope that it will apply to multiple versions of multiple window managers. Good luck out there.