I'm just wondering if you are having a problem with the OS not executing the jar file when clicked, or are you not setting the Main-Class: in the manifest file of the class path. As pointed out above, if the user doesn't have the file associations configured, there is not much you can do. However, there is nothing wrong with having a batch file or shell script to launch your program. ANT does this, for example.
Now I want to share it with people and make sure they can play it by clicking the jar file instead of the MS DOS batch file I created. This would mean the src folder will not be given along side with the Java jar file.
Using launch software to generate an executable for the target OS to launch the Java code behind the scenes seems like overkill for a small game.