Disable Preview.app annoying delete file sound?

"You can't, kinda

The sound you are hearing is actually the sound made by Finder deleting the file.

If you have some kind of vendetta against that sound in general, you can just delete it from the system files. That way, deleting files will be silent.

These instructions actually modify system files, so make sure you are careful. Anything you do here can be reverted by simply 'installing' Snow Leopard over the top of your existing install. This will repair all the system components, while leaving your applications and user files in place.

Navigate to /System/Library/Components. The easiest way to do this is to use the key combination Command + Shift + G, and copy-and-pasting in that path.
Right click CoreAudio.component, and select 'Show Package Contents'.
Now, navigate to Contents/Resources/SystemSounds/Dock
Delete drag to trash.gif. You would be asked to authenticate yourself.

Now, restart Finder by running killall Finder in Terminal, or just restart your computer."