ConnectionManger.php

<?php

namespace Your\Namespace;

use SilverStripe\Core\Config\Configurable;
use SilverStripe\ORM\DB;

/**
 * Class ConnectionManager
 * @package Your\Namespace
 */
class ConnectionManager
{
    use Configurable;

    /**
     * @var array
     */
    private static $alternate = [
        'type' => 'MySQLDatabase',
        'server' => 'localhost',
        'username' => 'username',
        'password' => 'password',
        'database' => 'database',
    ];

    /**
     *
     */
    public static function connect_default()
    {
        DB::connect(DB::getConfig('default'));
    }

    /**
     *
     */
    public static function connect_alternate()
    {
        if (!DB::getConfig('alternate')) {
            DB::setConfig(static::config()->get('alternate'), 'alternate');
        }

        DB::connect(DB::getConfig('alternate'));
    }
}

Use Case

use Your\Namespace\ConnectionManager;

class ...
/** your code */
ConnectionManager::connect_alternate();

$query = SQLSelect::create();
// build and execute your query to the non-SS database

ConnectionManager::connect_default();

/** end your code */