Would it help to restore and mount the controlfile? Then from the datafile names one might be able to guess at the tablespace names.

Also, in mount mode can you offline (or even offline-drop) all the datafiles that you don't want,

THe name of the undo tablespace will be in the spfile.

1. Create a basic init.ora file with only one parameter "db_name"
   
2. Start the instance in nomount mode, restore spfile to a pfile and shutdown the instance
   

   SET DBID=${DBID};
   STARTUP NOMOUNT pfile=${WORKDIR}/init.ora;
   RESTORE SPFILE TO PFILE '${WORKDIR}/init.ora' FROM '${SPFILE}';
   SHUTDOWN ABORT;

   
   
3. Memorize the undo tablespace(s) and modify the parameters accordingly to the new server (*dest, memory parameter, cluster->stand alone db...)
   
4. Start the instance in nomount mode, restore the control file, mount the instance, and catalog the backup files
   

   SET DBID=${DBID};
   STARTUP NOMOUNT PFILE=${RESTODIR}/init${ORACLE_SID}.ora;
   RESTORE CONTROLFILE FROM '${CTLFILE}';
   ALTER DATABASE MOUNT;
   CATALOG START WITH '${BACKUPDIR}' NOPROMPT;
   CROSSCHECK BACKUP;

   
   
5. Retrieve the file names for the tablespaces you want to restore ($UNDOTBS contains the undo tablespaces you retrieved in step 3, $TABLESPACES the tablespaces you want to restore and $DATE the date to recover)
   

   select file#, name
   from v$datafile
   where creation_time <= to_date('${DATE}','YYYYMMDDHH24MISS')
     and ts# in ( select ts# from v$tablespace 
                  where name in ('SYSTEM','SYSAUX')
                     or name in (${UNDOTBS})
                     or name in (${TABLESPACES}) )
   /

   
   
6. Retrieve the name of the tablespaces you don't want to restore (=> $TBSNORESTO)
   

   select name
   from v$tablespace
   where name not in ('SYSTEM','SYSAUX')
     and name not in (${UNDOTBS})
     and name not in (${TABLESPACES})
     and included_in_database_backup = 'YES'
   /

   
   
7. Execute the "SET NEWNAME" command for all these files as well as temporary files (retrieved from v$tempfile) and the "ALTER DATABASE RENAME FILE" for the redo log files.
   
8. Restore, recover the database and open the database
   

   SET UNTIL TIME "TO_DATE('${DATE}','YYYYMMDDHH24MISS')";
   RESTORE DATABASE SKIP FOREVER TABLESPACE ${TBSNORESTO};
   SWITCH DATAFILE ALL;
   RECOVER DATABASE SKIP FOREVER TABLESPACE ${TBSNORESTO} DELETE ARCHIVELOG;
   ALTER DATABASE OPEN RESETLOGS;

   
   
9. For all tablespace in $TBSNORESTO drop it with option INCLUDING CONTENTS AND DATAFILES CASCADE CONSTRAINTS
   
10. Recreate the temporary files: for all tablespaces and files retrieved by the following query:
    

    select ts.name, f.name
    from v$tempfile f, sys.ts$ ts
    where f.ts# = ts.ts#
    /

    
    Execute
    

    ALTER TABLESPACE <tbsname> ADD TEMPFILE <new tempfile name>;
    ALTER TABLESPACE <tbsname> DROP TEMPFILE <the original tempfile name>;

    
    
11. Export the schema