So, using Order ID makes you Order. It just does. If you want to not be Order, use another ID. Pirate, Freelancer... I actualy made a faction like this once, that wanted to cover the whole of sirius from Nomads. ORDO|. Pirate ID suited me as I could kill anyone who stood in my way.
Moreover, you want to use Order gear? Like, Osiris and Resheph? And not be Order? You know, to use those ships, you have to be Order or allied with special permission to use them. If you do not have the permission, you will be targeted and shot down by Order agents.
I like how you think of it, but using Order stuff and ID and not being Order... that just does not work.