Custom Nav Menu Walker class which outputs a select dropdown menu with focus on taxonomies instead a regular list-based one.

dropdown-menu-walker.php

<?php

if (!class_exists('_my_dropdown_menu_walker')) :

    class _my_dropdown_menu_walker extends Walker_Nav_Menu {

		// don't output children opening tag (`<ul>`)
		function start_lvl( &$output, $depth = 0, $args = array() ) {
		}

		// don't output children closing tag    
		function end_lvl( &$output, $depth = 0, $args = array() ) {
		}

		function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
			global $wp_query;

			$active = '';
			if ( $item->current || $item->current_item_ancestor || $item->current_item_parent ) {
				$active = 'active';
			}

            // passed classes
            $classes = empty( $item->classes ) ? array() : (array) $item->classes;

            $class_names = esc_attr( implode( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item ) ) );

            // build html 
            // add product cat as value
			$value = '';
			if( !empty( $item->type ) && $item->type == 'taxonomy' && !empty( $item->object_id ) ) {
				$value = $item->object_id;
			}
			
			$href = '';
			if( ! empty( $item->url ) ) {
				$href = 'data-href="'   . esc_attr( $item->url ) . '" ';
			}
            
            
            $output .= $indent . '<option value="'. $value . '" class="' . $class_names . ' ' . $active .'" '.$href.'>';
	
			// add spacing to the title based on the current depth
			$item_output = '';
			if( $depth > 0 ) {
				$item_output .= str_repeat("&nbsp;", $depth * 4);
			}
			
			$item_output .= $item->title;

            // build html
            $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );	
			
			
			
		}

		// replace closing </li> with the closing option tag
		public function end_el(&$output, $item, $depth = 0, $args = array() ){
			$output .= "</option>\n";
		}
    }
endif;