If you are using the standard Windows explorer window to delete a file, then I don't think there is a way without mangling your OS. You can use programs to close the popup, like PTFB (www.majorgeeks.com/files/details/ptfb_(push_the_freakin_button).html) Or, you can use Command Prompt to do it without a popup, if you know how. Use something like "del /f /q C:\Users\USERNAME\Documents\trash_document.doc" to do this, but be careful, since you can wipe out vital files with a single press of the enter key if you don't know what you are doing.
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