I THINK this may help: (Make a backup first!)

In:-

includes/modules/pages/checkout_shipping

Open (in a suitable text/php editor)

jscript_calendar_head.php

Modify:

{ date: 'Y-m-d' }
to { date: 'd-m-Y' }

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

To get D-M-Y in your store, you need to modify the following sections in the english.php files in both your CATALOG and your ADMIN sections:

(This is the DEFAULT in a standard install of ZC and renders the date as M-D-Y)
PHP Code:
  @setlocale(LC_TIME'en_US.ISO_8859-1');
  
define('DATE_FORMAT_SHORT''%m/%d/%Y');  // this is used for strftime()
  
define('DATE_FORMAT_LONG''%A %d %B, %Y'); // this is used for strftime()
  
define('DATE_FORMAT''m/d/Y'); // this is used for date()
  
define('DATE_TIME_FORMAT'DATE_FORMAT_SHORT ' %H:%M:%S');

////
// Return date in raw format
// $date should be in format mm/dd/yyyy
// raw date is in format YYYYMMDD, or DDMMYYYY
  
if (!function_exists('zen_date_raw')) {
    function 
zen_date_raw($date$reverse false) {
      if (
$reverse) {
        return 
substr($date32) . substr($date02) . substr($date64);
      } else {
        return 
substr($date64) . substr($date02) . substr($date32);
      }
    }
  } 
Look CAREFULLY at the above and apply the shown changes BELOW for UK-Styled D-M-Y format).
PHP Code:
@setlocale(LC_TIME'en_UK.ISO_8859-1');
define('DATE_FORMAT_SHORT''%d/%m/%Y');  // this is used for strftime()
define('DATE_FORMAT_LONG''%A %d %B, %Y'); // this is used for strftime()
define('DATE_FORMAT''d/m/Y'); // this is used for date()
define('DATE_TIME_FORMAT'DATE_FORMAT_SHORT ' %H:%M:%S');

////
// Return date in raw format
// $date should be in format dd/mm/yyyy
// raw date is in format YYYYMMDD, or DDMMYYYY
  
if (!function_exists('zen_date_raw')) {
function 
zen_date_raw($date$reverse false) {
if (
$reverse) {
          return 
substr($date02) . substr($date32) . substr($date64);
} else {
  return 
substr($date64) . substr($date32) . substr($date02);
      }
    }
  } 
As there is no over-ride system in ADMIN, just edit/over-write the original english.php file.

For /includes/languages/english.php , you should save the edited copy to your custom folder.

IMPORTANT NOTE:

Lower down in english.php, there are additional date defines (such as date of birth define text) that indicate to the shopper, that the format is MDY. Find these and alter them so they indicate the date format to now be DMY