A great read thanks, as this addressed a similar issue I was having.
In my case the menu icon had to open a script located in the home directory which in turn opened a browser with a web page which could not be set using a browser home page options. Using home page option on a remastered ISO results in a browser's first use screen instead of the desired web page.
I found the cliorx command very helpful in ensuring the program was executed, unfortunately the wrapper opened two windows, always one blank terminal window and another window with the program regardless of whether the final program was one with a gui or a command line script.
In the end I settled for a /usr/local/share/applications/program Desktop Entry like
"Exec=./myscript" or
"Exec=/home/tc/myscript"
myscript was made executable with chmod a+x myscript.sh
then of course within myscript a simple command to open a web page directly on opening
/usr/local/bin/browser
http://apod.nasa.gov/apod/astropix.html (or whatever)
I found other commands to work also like tc-run
Not sure why cliorx doesn't open the app in one window but the above works for me and will use this unless someone can show me a better way.