Exactly do what Knotts does and offer a year round refillable cup and stations to refill it. What's Disney afraid of? Some APer drinking more than his $50 allotment of coke? It costs Disney like a couple of cents to fill it.If Disney was serious, they would do what other theme parks do. Sell a refillable container that comes with a reusable straw.
Heck, Universal offers Coca-Cola products. They have Freestyle Machines that have a barcode/RFID reader. If the cup is valid that day, the machine will allow the drink products to be dispensed in a self service fashion. If you try any other cup, the machine won't dispense.
Other parks do similar things.
But this way, no trash, no flimsy lids, no paper cups and no disposable straws to deal with.