At first I thought to withhold this answer because it is for OS X only. I thought I would look silly if someone posted a cross-platform solution. But it doesn't look like that's going to happen, so I feel I might as well show how it can be done on an OS that makes it easy. The only tricky bit here is that you have to be aware that the OS X Trash won't accept two files with the same name.
Can't show any results here; this code is only for its side-effects. However, you can play with using a piece of code that was one of my unit tests. The code should be evaluated a few times, say three, to verify that multiple files with the same name can be moved to Trash.
Remember this is for OS X only.