Once the category is selected it would be pretty easy with the help of wp_nav_menu to check what category is currently selected using is_category and then load the menu you need. This would be defined in your page template or header (depending on where your menu is loaded)
if (is_category('category 1')) {
wp_nav_menu( array('menu' => 'category1-nav') );
} else if (is_category('category 2')) {
wp_nav_menu( array('menu' => 'category2-nav') );
} else if (is_category('category 3')) {
wp_nav_menu( array('menu' => 'category3-nav') );
}
You will need to define the different menu’s in your functions.php like this :
register_nav_menus( array(
'category1-nav' => 'Category 1 Navigation',
'category2-nav' => 'Category 2 Navigation',
'category1-nav' => 'Category 1 Navigation'
) );
Once you’ve defined the menu’s you can set them up under Appearance > Menu’s in the admin area.