How force specific table to not logging (for all DML)?
If you are so concerned about the redo logging volume, you can consider writing the logon/logoff audit records to a file instead, using UTL_FILE for example.

As an aside, I'd be hard pressed to believe that updates of the audit table generate more logs than other activities in the database. This would mean that your users mostly log on to the system and then immediately log off, without doing much else.