Mute Emergency alert in Google Now (without removing it)
If you go to google now, and then go to settings (the three dot menu button if its a soft key) theres a section that says notifications. That section has a part titled Urgent Updates and has the option to set a ringtone or turn on vibrate. As far as I know this should change the sound for the alert since it says urgent updates include public alerts. Just note, I am using KitKat so if you don't have the latest version of google now it could be different. 
EDIT: I just realized this question was asked a year ago so the answer details a newer version