Hi Ded,
I don’t think that using its own cookies would work unfortunately – cookies are locked to a specific website and, to preserve privacy and avoid a single point of vulnerability, RapID uses a different authenticator for each site. (i.e. each site only trusts certificates issued by itself and the app has a secret key and certificate for every site you enrol).
WordPress uses cookies for each site to track the current session, but it can be quite complex to change reliably. Best to try one of the numerous plugins that purport to manage session duration for your site. Just search for ‘session timeout’ for example. I’ve not tried any of these myself though.