Blender can now be launched using /usr/share/applications/blender.desktop but this launcher runs it in windowed mode, would you please add another shortcut to run it in windowed mode too ? To run blender in fullscreen mode you just have to run it with the -W option (-w is for the windowed mode).
There's no keyboard shortcut to switch the mode? If not, then maybe ask upstream to add one, because that's the right solution (unlike installing redundant desktop files).
I'm not sure if that's _this_ useful, you might just edit the .desktop file yourself.