Why use conversion, if you can simply configure the session for all known date types:

alter session set nls_date_format = 'YYYY-MM-DD HH24:MI:SS';
alter session set nls_timestamp_tz_format='YYYY-MM-DD HH24:MI:SS.FF6 TZR';
alter session set nls_timestamp_format='YYYY-MM-DD HH24:MI:SS.FF6';