You will still need a preservative. You ALWAYS need a preservative. The inertness or non-inertness of the materials in any cosmetic, even a powder cosmetic, is completely irrelevant - the preservative is needed to kill the mold and/or bacteria that are introduced to the cosmetic by consumer use.
This is a formulation decision that is largely CYA - if a consumer believes that she has been harmed by your product, one of the first things that will happen is a micro test of the powder product. If they find any mold and/or bacteria, your company will be on the hook for a large legal settlement.
This development is fairly recent - 20 or 30 years ago, preservatives weren’t used in inert/anhydrous cosmetics much, if at all. The preservative companies have been greatly helped by the plentiful consumer lawsuits.