Only execute specific shortcodes

It’s easier to remove specific shortcodes than it is to remove_all_shortcodes() and enable specific shortcodes.

To disable specific shortcodes from display everywhere, you would use the following:

<?php
add_filter( 'the_content', 'oxo_remove_shortcodes', 0 );

function oxo_remove_shortcodes( $content ) {

    /* Add the shortcodes that you would like to remove to the array below. */
    $shortcode_tags = array(
        'shortcode_1',
        'shortcode_2',
        'shortcode_3'
    );

    /* Remove each of the shortcodes listed above. */
    foreach ( $shortcode_tags as $shortcode_tag )
        remove_shortcode( $shortcode_tag );

    /* Return the post content without the shortcodes listed above. */
    return $content;
}

ALTERNATIVE

Depending on why you only want to enable a few shortcodes, you may be able to get away with creating a filter that checks if the content has_shortcode() from an array, and then strip_shortcodes() from the content, if it does not.

NOTE: a filter like that would be server intensive, and time consuming in terms of site performance.