I just noticed that you mentioned cold backups in your question. There's usually only one reason to make cold database backups – your database is in
NOARCHIVELOG mode. If your database is in
NOARCHIVELOG mode, you cannot use TSPITR, because it requires the database to be in
ARCHIVELOG mode to perform incomplete database recovery using archive logs.
All you can do in
NOARCHIVELOG mode to restore the tablespace(s) to some point in the past is use the previous backups of database, but in this case you can only restore the database (and therefore tablespaces) to the points in the past when these backups were made, because no archive logs are available and thus no recovery is possible.
This means that to restore your tablespace (database) as it existed two days before, you need to have a full backup of database made two days back, or you need a full database backup made more than two days back and all incremental backups of database up to two days before.
If you have all the backups required, you can duplicate your database to a different host, restoring it until two days before (or earlier), extract the tablespace(s) you need to restore (do you remember we can't recover in
NOARCHIVELOG mode?), and then move this tablespace(s) to the destination database.
You can duplicate the database using
DUPLICATE RMAN command (see the chapter "Creating and Updating Duplicate Databases with RMAN" in Database Backup and Recovery Advanced User's Guide).
You can use RMAN to move tablespaces to a different database using Transportable Tablespaces.