Change onclick function using javascript?

Better way:

var check = true;
function fn(){
   if(check)
     {
        alert(...);
        check = false;
     }
   else return false;
}

    $(window).load(function(){
        $("#check_box").change(function fn() {        
            alert("TEST");
            $("#check_box").attr("onclick","return false;");
            //change from `onclick="fn()"` to `onclick="return false;"`
        });
    });

$(window).load(function(){
    $("#check_box").change(function fn() {        
        alert("TEST");
        //change from `onclick="fn()"` to `onclick="return false;"`
        this.setAttribute("onclick","return false;");
    });
});

It can be solved in two ways, if you are using jQuery

$('#check_box').on('click', function(){
    $(this).attr('onclick', 'return false;');
})

or if you want to use vanilla / EcmaScript 5

document.querySelector("#check_box").addEventListener('click', (function(){
    this.setAttribute('onclick', 'return false;');
})();)

You can use jQuerys on a off functions

http://jsfiddle.net/8tq300mk/

I believe you have already answered your own question.

<input type="checkbox" id="check_box" name="check_box" value="Shared" onclick="return false">

is completely valid code.

You can use $(this).attr('onclick', 'return false;'); as shown below:

$(window).load(function(){
    $("#check_box").change(function() {        
        $(this).attr('onclick', 'return false;');
    });
});

Here's an updated version of your JSFiddle.

$(window).load(function(){
    $("#check_box").change(function fn() {        
        alert("TEST");

        $("#check_box").click(function() {
            return false;
        });
    });
});

Hope this helps.