WordPress: Extend Nav Walker Class for $terms seach

gistfile1.php

<?php
/**
	* Taxonomy Drop Down with hierarchical view using $terms
	* http://wordpress.stackexchange.com/questions/73583/taxonomy-drop-down-with-hierarchical-view-using-terms
*/
// Equipment Category Dropdown, thanks https://gist.github.com/2902509
class Walker_SlugValueCategoryDropdown extends Walker_CategoryDropdown {

        function start_el(&$output, $category, $depth, $args) {
        $pad = str_repeat('&nbsp;', $depth * 3);

        $cat_name = apply_filters('list_cats', $category->name, $category);
        $output .= "\t<option class=\"level-$depth\" value=\"".$category->slug."\"";
        if ( $category->term_id == $args['selected'] )
            $output .= ' selected="selected"';
        $output .= '>';
        $output .= $pad.$cat_name;
        if ( $args['show_count'] )
            $output .= '&nbsp;&nbsp;('. $category->count .')';
        if (isset ( $args['show_last_update'] ) ) {
            $format = 'Y-m-d';
            $output .= '&nbsp;&nbsp;' . gmdate($format, $category->last_update_timestamp);
        }
        $output .= "</option>\n";
    }
}
?>
<h2><?php _e('Categories:'); ?></h2>
<form role="search" method="get" id="equipfilter" action="<?php bloginfo('url'); ?>">
        <fieldset>
            <?php
            $dropdown_args = array(
                'taxonomy'      => 'software_categories',
                'name'          => 'Categories',
                'show_option_none'  => 'Choose category',
                'show_count'        => 1,
                'orderby'       => 'name',
                'hierarchical'      => true,
                'echo'          => 1,
                'walker'            => new Walker_SlugValueCategoryDropdown);

            wp_dropdown_categories( $dropdown_args );
            ?>
        </fieldset>
        <input type="submit" id="filtersubmit" value="Search" />
    </form>

    <h2><?php _e('Platform:'); ?></h2>
<form role="search" method="get" id="equipfilter" action="<?php bloginfo('url'); ?>">
        <fieldset>
            <?php
            $dropdown_args = array(
                'taxonomy'      => 'software_platform',
                'name'          => 'Platform',
                'show_option_none'  => 'Choose platform',
                'show_count'        => 1,
                'orderby'       => 'name',
                'hierarchical'      => true,
                'echo'          => 1,
                'walker'            => new Walker_SlugValueCategoryDropdown);

            wp_dropdown_categories( $dropdown_args );
            ?>
        </fieldset>
        <input type="submit" id="filtersubmit" value="Search" />
    </form>

    <h2><?php _e('Audience:'); ?></h2>
<form role="search" method="get" id="equipfilter" action="<?php bloginfo('url'); ?>">
        <fieldset>
            <?php
            $dropdown_args = array(
                'taxonomy'      => 'software_audience',
                'name'          => 'Categories',
                'show_option_none'  => 'Choose audience',
                'show_count'        => 1,
                'orderby'       => 'name',
                'hierarchical'      => true,
                'echo'          => 1,
                'walker'            => new Walker_SlugValueCategoryDropdown);

            wp_dropdown_categories( $dropdown_args );
            ?>
        </fieldset>
        <input type="submit" id="filtersubmit" value="Search" />
    </form>