if the translation is only for the archive widget, a filter function might work (to be added to functions.php of the theme):
add_filter('get_archives_link', 'translate_archive_month');
function translate_archive_month($list) {
$patterns = array(
'/January/', '/February/', '/March/', '/April/', '/May/', '/June/',
'/July/', '/August/', '/September/', '/October/', '/November/', '/December/'
);
$replacements = array(
'jan', 'feb', 'mar', 'apr', 'may', 'jun',
'jul', 'aug', 'sep', 'oct', 'nov', 'dec'
);
$list = preg_replace($patterns, $replacements, $list);
return $list;
}