Uninstalling Oracle Components on Production
have the datafiles from the currently active production database
  restored on the new database, then change over to the newly populated
  database on production


This will not work at all, unless you meant the transportable tablespace method and you intend to restore user tablespaces, and you create the new database using different binaries without the unnecessary options.

Sure, you can do this with TTS. Or export/import. These methods require downtime.

Or you could just remove options from the existing database. It all depends on the components you want to remove if you need downtime for this. 

Some components you can remove at binary level (which requires a database shutdown) using chopt starting with version 11.2 (which is the lowest currently supported version):

Chopt Tool

For example, do disable Partitioning, shutdown the database, then:

chopt disable partitioning


The removal of other options ususally include running scripts provided by Oracle and/or dropping schemas.

For example to remove APEX, you run the below in a regular (non-cdb) 12.2 database:

$ORACLE_HOME/apex/apxremov.sql


More details at (referring this blog post of an Oracle employee, because I could not find all this nicely collected together in the official public documentation):

Component Clean Up Series