uses ShellApi;

function SHDeleteFiles(const aSource: string): Boolean;
var
  SH: SHFileOpStruct;
begin
  FillChar(SH, SizeOf(SH), #0);
  SH.Wnd := 0;
  SH.wFunc := FO_DELETE;
  SH.pFrom := PChar(aSource + #0#0);
  SH.pTo := #0#0;
  SH.fFlags := FOF_MULTIDESTFILES or FOF_SILENT or FOF_NOCONFIRMATION;
  SH.lpszProgressTitle := '';
  Result := SHFileOperation(SH) = 0;
end;

그냥 Shell을 이용해서 하는겁니다...
허접하지만 쓰실만 할듯...
더자세한것은 MSDN의 SHFileOpStruct를 참고하세요...