That is not a problem. You will not actually be sending you order to any particular fulfillment center in your state, it just goes to whatever fulfillment center Amazon determines based on your ship from location, inventory packaging, and Amazon's location-based demand for your product (whether your state has a fulfillment center or not is irrelevant).
What happens if there is no fulfillment center by me?
Where does my shipment go if there's no FC in my state?
