changing permalink for custom template in posts of a certain category

You can achieve this via the Rewrite API‘s add_rewrite_endpoint:

function wpa89344_add_presentation_endpoint(){
    add_rewrite_endpoint( 'presentation', EP_PERMALINK );
}
add_action('init', 'wpa89344_add_presentation_endpoint');

Then in your template or wherever you differentiate a presentation vs normal view, check the global $wp_query for the presence of the presentation query var:

global $wp_query;
if( isset( $wp_query->query_vars['presentation'] ) ){
    include(TEMPLATEPATH . "/single_wide_report.php");
} else {
    include(TEMPLATEPATH . "/single_normal_report.php");
}

Note that you need to visit the permalinks settings page after adding the endpoint to flush permalinks and create the new rewrite rules.

EDIT- Output of $wp_query in single.php: