I will need to remove dioxane form the solution. However, if I don't use rotary evaporator, Can i use open air-drying instead? Are there any other methods to eliminate dioxane form mixture or solid precipitate?
Yes, you can use open air-drying with slight heating to accelerate the process. But you must take care about an effective ventilation as dioxane is highly flammable, poisonous and can form explosive peroxides. Drying in a stream of nitrogen preffered.
coconut charcoal - there is a drinking water method (US EPA) that uses solid phase extraction cartridges packed with charcoal to remove 1,4-dioxane from water. It will also remove many other organic compounds though, so I'm not sure if it would be applicable to your application. Link is below. You could also just try running through a Brita water filter as low cost test. If you can't use filtration you could use heat and sparging with air.