Make the entry 3/4” and put it on your deer call mandrel. Hold it on a 4 jaw chuck with pin jaws when you need to flip it.
Make sure you use a very sturdy material. The hunter will want this to be thin so it resonates well. Thin wood in a hunting situation is going to be very prone to getting crushed.
Tough task. This is why you often see horn used for this kind of job.