I decided to put the audio as a simple plug-and-play script whenever the bullet is spawned. To do this, it needs the script and an audio source.
After adding these, I created a script that looks for the audio source and then pulls the clip, does a random.range to the audio to give it some variance, and then plays the audio clip.
The only flaw was whenever the game object gets destroyed, there is an immediate cut off. To prevent this, I set the bullets up to go to 0 velocity, remove their colliders, and then destroy themselves after 0.5f seconds.
Now the audio plays all the way through and the weapons can be easily added. You might want to reduce the volume or pipe the audio through the audio mixer to control levels.