I would think twice about doing this. For starters, it will be really slow if you connect an external drive to an airport extreme - like less than 30MB/sec. See this:
https://forums.macrumors.com/threads/1747622/
But putting the iTunes library on a network drive really doesn't work very well. I did it on a Time Capsule for awhile and finally gave up. Took awhile for video to start playing, was awkward to skip through it, and it would stutter/pause at times.
If you decide to try it anyway, be sure that you locate the iTunes database (.itl file) on the shared disk. The default location for this file is on the computer itself. If you leave it in the default location and the connection to the shared drive is broken for any reason, you will have a corrupt library. That can be a real pain to fix - happened to me twice.
After trying various methods with libraries on shared drives I gave up, got a Mac Mini for an iTunes server and have been very happy with it.