The simplest solution would probably be to use a word boundary (\b) like this:
s.replace(/\b0+/g, '')
This will remove any zeros that are not preceded by Latin letters, decimal digits, underscores. The global (g) flag is used to replace multiple matches (without that it would only replace the first match found).
$("button").click(function() {
  var s = $("input").val();
  
  s = s.replace(/\b0+/g, '');
  
  $("#out").text(s);
});
body { font-family: monospace; }
div { padding: .5em 0; }
#out { font-weight: bold; }
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div><input value="02-03, 02&03, 02,03"><button>Go</button></div>
<div>Output: <span id="out"></span></div>