SAML SSO with Swing Client, webapp SP and IdP using spring-security-saml2-core

My project is currently uses spring-security as follows:

• Has a webapp service provider (SP)
• SP uses LDAP as IdP username / password as auth tokens
• Has a Swing based fat client (FC) that accesses SP using SOAP/HTTP
• Has a REST client (RC) access the SP using HTTP
• FC and RC both authenticate with SP via WSS using spring-security and basic authentication

I would to enhance my project to support SAML2 SSO using spring-security-saml2-core and an external IdP such as ssocircle.com or onelogin.com but I am not sure if it is possible and if so how. Specifically I have the following questions:

• How to handle the Swing based fat client (FC) in the SSO scenario? How does it change to support SAML2 SSO?
• What would be the authentication mechanism between FC and SP? Would it still be WSS using spring-security?

TIA for any high level advice on how to support SAML2 SSO in my scenario.