You can manually create a new table in your phpMyAdmin on server (it's obviously your site that you will not move frequently to a new server) or, of course, you can hook table creation with theme installation or similar. Wordpress use the object/class $wpdb for achieving any query within Wordpress database. There you can see how to execute any query within WP database. So, I would use something like this:
global $wpdb; // Object must be globalized.
CREATE TABLE IF NOT EXISTS ".$wpdb->prefix."new_table (
id bigint(20) unsigned NOT NULL AUTO_INCREMENT,
post_id bigint(20) NOT NULL,
image_url varchar(250) NOT NULL,
PRIMARY KEY (id),
KEY post_id (post_id)
) ENGINE=MyISAM DEFAULT CHARSET=latin1 AUTO_INCREMENT=1 ");
You can put it in a function and hook it to theme_init for instance or something similar. Change fields by your preferences. Another way is using dbDelta() function, which has some specific rules and because of that I don't see the right reason of using it (maybe there is some and I'm wrong) - you can find all about it here (I can't put more permalinks because of rep, sorry :D)
After creating the table, you can manipulate it any way you want - you can hook registering that attachments into new table. You can also hook some function that will prevent putting attachments into the posts-table.
Because of the small number of columns (like postmeta table, for instance) I guess it's lightweight and therefore there have to be some performance improvement in manipulating with that images.