How do you disable an application specific hotkey, for example, "Command-P"?

This can be achieved by remapping the Print shortcut to a different shortcut that is out of the way, unused and unlikely to be pressed.

1. Open System Preferences → Keyboard → Shortcuts → App Shortcuts.

2. Click + to add a new shortcut.

3. Application: All Applications

   Menu Title: Print… _{(that's a 'proper' ellipses by the way, use copy-paste if necessary)}

   Keyboard Shortcut: Set it to something out of the way.

   

4. Click Add.

Now, the Print command is set to a random keyboard shortcut, freeing up ⌘P.

You can also use defaults to change the shortcut to something like U+200B (ZERO WIDTH SPACE):

defaults write -g NSUserKeyEquivalents -dict-add Print... '\U200b'

nil would be triggered when pressing n in some applications like Audacity and \0 would be triggered when pressing any key in Safari in 10.9.

I use a shell script like this to configure the shortcuts:

defaults write -g NSUserKeyEquivalents '{
"Show Previous Tab"="~@\Uf702";
"Show Next Tab"="~@\Uf703";
"Minimize"="\U200b";
}'
defaults write com.apple.Finder NSUserKeyEquivalents '{
"Show Package Contents"="@\r";
}'