I'd think it's unlikely Microsoft would permit this level of manipulation with the GUI/file management system--seems like it would be a gaping security hole.
It's not nearly as seamless as what you're looking for, but the next-best thing I can think of is to add a shortcut to your 'Deleted Files' folder to the Windows 'Send To' folder, per the instructions here:
You’ve seen the SendTo folder in action any time you right-click a file and select the Send To folder from the context menu. What you might be unaware of is that you can customize the items in this menu.
To get to the SendTo folder, you’ll need to open up an Explorer window, and then paste in the following to the address bar:
Let’s say you wanted to add an item to the Send To menu to open files in Notepad. You could just drag a shortcut to Notepad into this folder, or create a new shortcut.
For your purposes, create a shortcut to the 'Deleted Files' folder in this ...\SendTo folder.