I finally got it figured out.  For future reference,  

To Log note in the chatter.  There is a built-in function available named "message_post".  

There's no need to directly call the built-in wizard, I can create my own wizard and just write an action to use "message_post".  

"message_post" is available by _inherit = ['mail.thread', 'mail.activity.mixin'], which is needed for the xml form view to display chatter section anyway.  

Example:  

# This method overrides action_cancel and calls my own wizard.
def action_cancel(self):
    view = self.env.ref('mymodule.xmlid_of_wizard')
    wiz = self.env['action.cancel.confirm'].create({})     
    _logger.info("Action Cancel is overrided.")
    super(Picking, self).action_cancel()
    return {
        'name': _('Your Reason to Cancel?'),
        'type': 'ir.actions.act_window',
        'view_type': 'form',
        'view_mode': 'form',
        'res_model': 'action.cancel.confirm',
        'views': [(view.id, 'form')],
        'view_id': view.id,
        'target': 'new',
        'res_id': wiz.id,
        'context': {'parent_model': self._name, 
                    'parent_id': self.id},
       }


# Method in the wizard to Log
def action_confirm(self):
    parent = self.env[self._context['parent_model']].browse(self._context['parent_id'])
    msg = "Log to write"                          
    parent.message_post(body=msg)