You can nil the OnClick event handler while changing a radiobutton state programmatically:

procedure TForm1.Button6Click(Sender: TObject);

var

  Save: TNotifyEvent;

begin

  Save:= RadioButton2.OnClick;

  RadioButton2.OnClick:= nil;

  RadioButton2.Checked:= not RadioButton2.Checked;

  RadioButton2.OnClick:= Save;

end;