Non-English date format - is there a simple solution?

To me and my potential users, English is good enough for the overall interface. So I am not interested in translating the whole site. But when I use a CCK date field, I cannot use a long date format and have the names of the day or the month shown in a non-English language (Danish).

I have activated the Locale core module and tried to install the Internationalization module. But when I go to admin/settings/date-time/locale, select "Dansk" and press the search button, I still see the English names.
I have searched drupal.org thoroughly withaout finding any simple solutions. Are there any?
In principle, I could try to change the default language of the (UNIX) server. Would that be a way?