Hi,
In order to change the connection string you should not change the session state connection. This is for changing the default session storage which we currently do not support. You should look into the Gizmox.WebGUI.SQLManager.Site\Resources\Data\SQLManager.xml configuration file which allows you to define multiple database connections combining them on the same management console. You will find in this file a connection string template which is used in-order to connect to the database.
Sincerely,
Guy