If the options of dropdown are static, then you can connect onchange event of parent dropdown and reload the values of second dropdown using jquery.

$col["name"] = "firstcolumn";
...
$col["editoptions"]["onchange"] = "function(){ update_second(); }"


$col["name"] = "secondcolumn";
...

and in JS code

<script>
function update_second()
{
  if ($('#firstcolumn').val() == 1)
  {
    $('#secondcolumn').html('');
    $('#secondcolumn').append('<option value="cat-a">Cat A</option>');
    $('#secondcolumn').append('<option value="cat-b">Cat B</option>');
    $('#secondcolumn').append('<option value="cat-c">Cat C</option>');
  }
  else if ($('#firstcolumn').val() == 2)
  {
    $('#secondcolumn').html('');
    $('#secondcolumn').append('<option value="cat-a">Cat A</option>');
    $('#secondcolumn').append('<option value="cat-b">Cat B</option>');
  }
}
</script>