switch theme on fly

You can use Theme Switch and Preview.

If you are up for coding this yourself, you can use the template and stylesheet filters.

E.g.: to switch to Twenty Ten:

function custom_load_twenty_ten_template() {
    return 'twentyten';
}

function custom_load_twenty_ten_stylesheet() {
    return 'twentyten';
}

add_filter( 'template', 'custom_load_twenty_ten_template' );
add_filter( 'stylesheet', 'custom_load_twenty_ten_stylesheet' );