The best word for "audio" that I could think of is vox.
There are several words for sound, but vox sounds more neutral to me than canor, clamor, or strepitus, for example.
However, vox is not easily recognized as a technical term "audio" as opposed to "sound" or "voice" when the distinction is important, so beware.
The word "audio" of course comes from Latin and has made its way to a number of languages, but I would advice against using the word in Latin.
One could treat it as a noun in analogue to volo, but I'm suspicious of that analogy.
I am even more suspicious of the noun audium.
If you want to use the verb audire without losing too much in style or intelligibility, I recommend audiendum.
The word "recording" is complicated, too.
The best noun I found was vivarium, but it might be too colorful for a technical term.
I used this word in the sense that a recording keeps a sound alive but confined, ready to be released, as if recorded audio was a caged animal.
You might be better off with a verb like conservare, condere, or similar.
Collecting these ideas, my suggestion for "audio recording" is vox conservata.
Sure, it sounds quite a bit like "pickled voice", but I don't see a way around connotations of this kind.
(I would like to see if someone else sees one!)
I answered the question as stated (and it is an interesting one).
Judging by the linked questions, you wanted to write something like this:
Take a look at this page with an audio recording of Hans Ørberg reading chapters from one to ten of Lingua Latina [per se illustrata].
Wording is a matter of taste, but I would work myself around the noun "audio" here.
I might render it like so:
In hac pagina capitula a primo ad decimum Linguae Latinae [per se illustratae] a Iohanne Ørbergio recitata invenies.