Just a point of clarification, is the question if airlines are not in one of the major alliances, or any alliance. Technically, AZ is in an alliance with CO in the EWR-FCO/MXP flights. CO is also aligned with NW, AS, HP, CM, etc, but it is not a formalized grouping since as far as I am aware CM is not aligned with AS.
I would find it difficult to find no airline that is not in any bilateral alliance. I'm stating opinion, but airlines like Air Zimbabwe, Ghana Airways, don't seem to be operating in an alliance.