Except that he wants "a style and index.php styleswitcher" not just a style switcher. It is possible, but it isn't easy and it can become a mess. You would need a copy of the index.php file for every style you supply. Then in you main index.php, this is all that would be there:
$blog = 1;
include ( -set this to the path to the index.php you do want, based on the style name );
The every thing would be in the individual files for each style. Here's the kicker. If you want to change something, it has to be changed in every single one of those files.