I found the answer. This function returns info about the "copied" file. In my case, there will only be one file in the clipboard, so the following code calls the "GetPasteValue" function. I'm sure you get the idea.
  SourceFile := GetPasteValue ;
  PastedFileName := ExtractFileName(SourceFile);
  SourceExtn := UpperCase(ExtractFileExt(PastedFileName));
Function TfrmMain.GetPasteValue: String;
var
   f: THandle;
   buffer: Array [0..MAX_PATH] of Char;
   i, numFiles: Integer;
   sl: TStringList;
begin
  if Clipboard.HasFormat(CF_HDROP) then
  begin
    sl := TStringList.Create;
    try
      f:= Clipboard.GetAsHandle( CF_HDROP ) ;
      If f <> 0 Then
      Begin
        numFiles := DragQueryFile( f, $FFFFFFFF, nil, 0 ) ;
        sl.Clear;
        for i:= 0 to numfiles - 1 do
        begin
          buffer[0] := #0;
          DragQueryFile( f, i, buffer, sizeof(buffer)) ;
          sl.add( buffer ) ;
        end;
      end;
      if sl.Count > 0 then
         Result := sl.strings[0];
    finally
      Clipboard.close;
      FreeAndNil(sl);
    end;
  end
  else
  Result := 'NO CF_HDROP';
end;