Shortcode Placeholder Plugin

Of course. You need two things – a settings page, and a custom shortcode handler. The first is a little too broad to discuss in detail here, but this tutorial should help get you started. You can also check out the codex, or post back here with a new question if you really get stuck.

Now for the shortcode:

function wpse_203387_param_shortcode( $atts ) {
    // [PARAM name="data"], $atts will be an array of name => data pairs
    // [PARAM data], $atts will be a numeric array with one element, "data"

    // In this case, we just always grab the first value/data
    $name = array_shift( $atts );

    switch ( strtolower( $name ) ) {
        case 'youtubehome' : // [PARAM youtubehome]
            $data = get_option( 'theme_options' ); // This is purely for example, use the data structure/names that match your settings API config

            return $data['youtube_setting'];

        case 'anotherparam' : // [PARAM anotherparam]
            return 'something_else';
    }
}

add_shortcode( 'PARAM', 'wpse_203387_param_shortcode' );

Update: To allow other roles (capabilities) to update your settings:

function wpse_203387_options_page_capability( $capability ) {
    return 'edit_theme_options';
}

add_filter( 'option_page_capability_my-theme-settings-name', 'wpse_203387_options_page_capability' );