Single Sign-on between PS HR and PS FIN Environments with different Operator IDs

Need Some Expert Advice for the below situation:

I am trying to establish SSO between PS HR and PS FIN environments, but the Operator ID’s are different in both the environments.  So I would like to know which is the best and effective way to do from the below options:

Can I use PeopleSoft-Only SSO approach ? and manipulate the cookie value (PS_TOKEN) and retrieve the FIN OPR ID based on PS HR OPRID to authenticate the user Or Use Single Signon with Third Party Authentication approach? In both the approaches, do I need to setup a Public User on Web Profile for Allowing Public Access or so.