I would imagine Aurigny would keep their handling 'in house', probably the same for Blue Island. Luftie will probably go with the cheapest, but Aurigny have a good reputation as handling agents.
Don't see how an independent handling agent would facilitate pushback procedures. There's a hell of an investment needed to fund ground vehicles, probably why Flybe decided to hive off their handling to an outside agency. On the other hand, a cynic might think that they were engaged in running down their operations here (GCI).