You 'crudely' overwrite the old sound file, basically.
So first step would be to know the exact name of the sound you want replaced. And then, in World of Warcraft/Sounds/Spells, (if Sounds and Spells folders aren't there, you create them), you put in ANY replacement sound that you like and rename it to have exactly the same name as the old one.
Now when your WoW client looks for the sound to play, it will use the sound you provided.
Personally, I used WoWModelViewer to find the sound files, at the bottom of the list of models there's a dropdown, where instead of 'models' you'd choose 'OGG' and absolutely all the sound effects are there. If you're curious how one of them sounds, to know if it's the sound you're looking for, you save it and play it.
And before you know it, your game ends up sounding something like this-
https://www.youtube.com/watch?v=K1I9lgd7YuQ