Quit HipChat. Navigate to Applications > HipChat.app. Right-click HipChat.app and select "Show Package Contents".
You will now be browsing the contents of HipChat.app. Navigate to Contents > Resources > notify.wav. After you've found your new audio file and renamed it to notify.wav, copy it into that directory, replacing the existing one. Reopen HipChat and you're good to go!
Quit hipchat. Navigate to the following path:
C:\Program Files (x86)\Atlassian\HipChat4\localweb\assets\audio
Replace notify.wav with your new notify.wav sound file. Reopen HipChat.
There is an obvious downside to this approach: each time you update the Hipchat app, your new sound file will be overwritten. Therefore, it's recommended you back up your notify.wav file somewhere else (and bookmark this guide) so that you can repeat this process if need be.