Thanks Ameet!
It sounds like a very good solution, but unfortunately, Concurrent Employment is not activated in our system.
Looks like to activate External Person ID (using the CCURE PIDGN switch), I have to first activate Concurrent Employment (using the CCURE MAINS switch).
The documentation for CCURE PIDGN switch states that "When you activate the person ID in your system the first time, generate the Person ID infotype (0709) for all your employees using the HR_CE_GENERATE_PERSONID_EXT report."
Also, the documentation for CCURE MAINS switch states as a Requirement that "If you want to activate the Concurrent Employment functions in your SAP system, you must first contact SAP."
So to me it makes an impression that I cannot use CP object for just one employee, without activating the Concurrent Employment for all employees in the system, is that right?