If you go to a bike shop and ask for an empty bike box, they'll gladly give you one for free. Ask for the biggest one they have. Take off both wheels and turn your handlebars. Stuff three of your panniers in the gaps so you only check one item, and use your fourth as a carry-on. At the airport, they'll charge you an overweight fee. An overweight fee isn't much worse than checking a second bag, which you'd probably have to do if you used a smaller box that can only hold a bike that has couplers.
So my solution involves not bothering with the couplers.