I need to view the saved WiFi passwords on my non-rooted Android phone
This is not directly possible (as noted in the comment below your question).

You can let Google save them to their cloud:

Go to: Settings->Privacy and enable those two options:  


Back up my data (Back up application data, Wi-Fi passwords, [...]) 
Automatic restore


Also, say yes when you're prompted if you want to Restore data during the first time set up of your new SGS3. If you've done the first time setup already withouth that option enabled, then maybe the Automatic Restore settings does it afterwards (not tried yet, though).