It's very important that you're able to maintain your gallery yourself. If you're still afraid that anything could go wrong, just create the dump of your database with a tool like phpMyAdmin or MySQLDumper and download all gallery files to your local PC. Install a server software like XAMPP or WAMP, import the database dump, copy your gallery files to the htdocs directory, adjust the MySQL credentials in include/config.inc.php and apply the upgrade as described in the docs.
Of course somebody else could do all that for you, but when the next Coppermine version is released you're again depended that somebody performs the upgrade for you. As it's mandatory to create backups regularly, the main task applying an update is to overwrite the existing files on your server with a tool like FileZilla and then visit update.php in your browser while logged in as admin. That's all.