Make categories appear random

You could hook into the pre_get_posts action hook and set the posts’ order to random only for specific categories. Here’s a basic example on how to achieve so:

function sort_posts_randomly( $query ) {
    if ( ! is_admin() && $query->is_main_query() ) {
        if ( is_category( 'category id, slug, or name' ) ) { 
            // Sort the posts randomly
            $query->set( 'orderby', 'rand' );
        }
    }
}
add_action( 'pre_get_posts', 'sort_posts_randomly' );