The best way to solve it would be to not use a 3rd party library with your code. However, since that likely isn't an option, here's another way to solve it:
<script src="jquery.js"></script>
<script src="yourexternaljs.js"></script>
yourexternaljs.js:
(function($){
// you are free to use $ inside of this area without conflicting with anyone elses code.
$(document).ready(function(){
alert("dom is ready.");
})
})(jQuery.noConflict(true));
Per your edit, yes, you could go into jquery.js and change all references to window.jQuery and window.$ to whatever you want, it should only be in there 2-4 times.