Spraying is undesirable for a museum artifact as well as people and the environment. Also, spraying usually entails multiple sprays over time to kill anything in all its stages of life. Have you considered anoxic treatment of the windmill? NPS has published a Conserve-o-gram on anoxic treatment for pest management (attached). If you have a museum in your area that has an objects conservator on staff, it’s worth calling for some input.