Shrink table SYS.AUD$
Where did you 'read' that the procedure you state is necessary to shrink the table?
Yes, you should use dbms_audit_mgmt to relocate your audit table out of the SYSTEM or SYSAUX table space.  Not to shrink the table, but because that is best practice.
Is it an online operation?  What does the doc say?

Usage Notes
The following usage notes apply:
This procedure involves data movement across tablespaces. This can be a resource intensive operation especially if your database audit

trail tables are already populated. Oracle recommends that you invoke
the procedure during non-peak hours.

Should you move it back to the SYSTEM TS?  No.
Also, when considering shrinking table you need to remember that space that is freed up by deleting rows is still allocated to the table and will be reused by future inserts.  Unless a delete is a one-time cleanup and permanent reduction in the number of rows, a shrink table is worse than wasted effort because future inserts will just incur additional overhead to re-acquire the needed space.
But remember, relocating the table into its own TS is just good management, regardless of shrinking the table.
Also, you state you are on 11.2.0.4. That is out of support and long past time to upgrade.