wp_dropdown_categories() searching is not working with CPT, please review my code

Working drop down in search for CPT

<?php

  $categories = get_categories('taxonomy=custom-tax');

  $select = "<select name="cat" id='cat' class="postform">n";
  $select.= "<option value="-1">Select category</option>n";

  foreach($categories as $category){
    if($category->count > 0){
        $select.= "<option value="".$category->slug."">".$category->name."</option>";
    }
  }

  $select.= "</select>";

  echo $select;
?>

<script type="text/javascript"><!--
    var dropdown = document.getElementById("cat");
    function onCatChange() {
        if ( dropdown.options[dropdown.selectedIndex].value != -1 ) {
            location.href = "https://wordpress.stackexchange.com/questions/315973/<?php echo home_url();?>/category/"+dropdown.options[dropdown.selectedIndex].value+"https://wordpress.stackexchange.com/";
        }
    }
    dropdown.onchange = onCatChange;
--></script>