Multiple programs to process WAV files—Any potential issues?

Since metadata is inherent in Wav files, you can't actually avoid it, even if you want to. Even if you input no individual data, the structure is still all there. That's how they can tell what software you used to create the file! The thing about metadata in Audition is that you can alter it to say anything you want - yes you can even change the name of the software you used.

One difference with Audacity as far as wav files is concerned is that they are encoded using libsndfile (they tag the 'creator tool' line in the meta with it, so it's easy to tell. I can't see any other difference. But of course there's also nothing to stop you doing exactly the same thing with Audition - there's an option to use it for wav files if you want. It might well be worth saving your files using libsndfile - there are a lot of coding options, as you'll find if you explore the save panel. There's also an option to exclude metadata in your save, although it doesn't really mean this - it just means that the meta framework is empty. It really does clear it out though, so that may be worth experimenting with too.

Bottom line is that Audition can manipulate metadata far more extensively than Audacity can. All you need to do is find out which settings Audacity's libsndfile is using, and replicate those in Audition.