I don't think there's a way in the user interface but if you're comfortable with directly accessing the database and don't need to update any timelines/activities you can do something like:
UPDATE civicrm_case SET case_type_id = CONCAT(CHAR(1), '8', CHAR(1)) WHERE case_type_id = CONCAT(CHAR(1), '1', CHAR(1));
This would take the ones who have case type 1 and convert them to 8. You'd have to look and see what the existing numbers are:
select ov.label, ov.value from civicrm_option_group og inner join civicrm_option_value ov on (ov.option_group_id = og.id and og.name = 'case_type');
And of course do this on a test site first, and make a backup.