Oracle Upgrade Standard to Enterprise Edition
You can simply install Enterprise Edition in a different folder, and you can start the databases using that as ORACLE_HOME.

This way you can shutdown the databases running from Standard Edition ORACLE_HOME and startup databases using the Enterprise Edition ORACLE_HOME one at a time, whenever it is feasible.

But you will not be able to skip the install part. There is no official and supported method for converting an existing Oracle software installation from Standard to Enterprise Edition.