I’d been looking around for the best solution for this and most of what I had found either performed poorly or wasn’t quite random enough. Not so strangely in the end, the best solution was the most basic.
Note: This also works fine with the ActionScript 3 Vector() class.
For ActionScript:
function shuffleArray(array:Array):Array
{
  for (var i:int=0, len:int=array.length; i<len; i++)
  {
    var j:int = Math.round( Math.random() * (len-1) );
    var value:* = array[i];
    array[i] = array[j];
    array[j] = value;
  }
  return array;
}For JavaScript:
function shuffleArray(array) {
  for (var i = 0, len = array.length; i < len; i++) {
    var j = Math.round(Math.random() * (len - 1));
    var value = array[i];
    array[i] = array[j];
    array[j] = value;
  }
  return array;
}