[pgranados]

Ya lo resolví, si alguien necesita el código es:

Código Delphi [-]
use shellapi;
var
  ShOp: TSHFileOpStruct;
begin
  ShOp.Wnd := Self.Handle;
  ShOp.wFunc := FO_DELETE;
  ShOp.pFrom := PChar('RUTA'#0);
  ShOp.pTo := nil;
  ShOp.fFlags := FOF_NO_UI;
  SHFileOperation(ShOp);