The DeleteFile XCMD by David Conger is public domain software and may be freely distributed (with this documentation). No Finder replacement stack is complete without one!
When using ResEdit or another resource mover to put DeleteFile into your own stacks, be sure to move its associated ALRT and DITL resources. They are numbered 25057 and 23580 respectively and are both named "DeleteFile."
When invoked, DeleteFile presents the user with a stanard Get File dialog box. The type of files displayed by the dialog depend on the parameters passed to DeleteFile. Once a file has been chosen, the user is presented with an alert to confirm the choice to delete the file. If the user clicks "OK" the file is deleted.