I don't know what CA would do to stained would, but I do know that it is more difficult to have a clean look with CA, especially in your case since the model is intended to be displayed. A little run off and it will be very difficult to sand off the excess. Go with wood glue, you will have a lot more working time and it is very easy to clean off excess glue for a very clean look. Besides, your body will thank you for it: CA fumes are really really bad for you. I build my RC planes with wood glue with excellent results.