Is it possible to disable the "Deleting file" message and progress bar?
Of course it's possible. Set up a development environment, modify poll_cancel_action() in apps/fileop.c to not show the splash for deletion (as opposed to copying and moving) operations, compile a new binary for your device.
But keep in mind that disabling the progress splash won't let you do anything else while the operation is happening; the UI will just appear to hang until it's finished, and that's probably not what you want.
(Of course, changing that is also possible, but would require a substantial amount of work)