I have recently done this. You could use an Airport Extreme with external hard drive, but it will be much slower than the internal drive on a Time Capsule. See this:
https://forums.macrumors.com/threads/1747622/
So I used a Time Capsule for awhile, and it works fine, but there are a bunch of "gotchas". If, for any reason, the shared drive is not available while iTunes is running, then you have problems. This caused my iTunes Library to become corrupted a few times. There are many reasons why the disk might not be available - like when the computer goes to sleep while iTunes is running, then you wake it up in a different location.
Anyway, this finally got too annoying after a month or two so I gave up on it. I got a Mac Mini for an iTunes server, and it just sits there running iTunes all the time using home sharing. This works really well and does not have any of the issues mentioned above. If the MBA can't connect to the server, there are no problems, you just won't be able to access the library. And this solution also makes your library available to any other i-devices or computers for you and your guests. It also makes the library available all the time for an Apple TV.
I would really suggest this solution over putting your library on a shared disk, Apple has done a nice job of building this capability into iTunes. You could use an older Mac for this as well - many people use old core 2 duo machines as servers, but I wanted something new with a warranty that would be fast and last me a number of years.
Also, regardless of how you do this, you will want a way to regularly backup your library. This is more of a pain using a Time Capsule or Extreme. You would need to run the backup program on your MBA and all the data will flow over your network at the speeds in the thread I linked to above. You can't use time machine for this, so I used Carbon Copy. If you have a large library, a backup can take a long time and will tie up your MBA while it's running. With a dedicated server, the backup can be done to a local drive with Time Machine or CCC.