A possible alternative is to publish both Login modules, CB Login and K2 Login with this last module showed only with access to "Registered".
In this manner I've only the CB login and after the login I can see the "K2 login module", but with user already logged and so able to see the 4 K2 links.
I have two "logout" button, in CB module and in K2 module, and the link to modify K2 profile (and not CB), but these are minor problems.
However it is strange that with K2-CB Integration it is out of the door the main feature of K2: to write articles.
Furthermore I can show CB profile, but if I ask to modify values it is showed the list of the k2 fields.
=========
Last minute news.
In the k2 forum I have the confirm about this, it is mandatory to use K2 Login Module to add articles, also if after a CB login.
Thanks to everybody