Wait before ShellExecute is carried out?

I have a hopefully quick question: Is it possible to delay execution of ShellExecute a little bit?

I have an application with autoupdater. After it downloads all necessary files etc, it renames current files to *.OLD and the new as the previous. Simple enough. But then I need to delete those .OLD files. This 'cleanup' procedure is executed on MainForm.OnActivate (with a check if it is the first activate proc). But this apparently happens too fast (I get False from DeleteFile). This is the procedure:

procedure TUpdateForm.OKBtnClick(Sender: TObject);
const SHELL = 'ping 127.0.0.1 -n 2';
begin
  ShellExecute(0,'open',pchar(SHELL+#13+Application.ExeName),nil,nil,SW_SHOWNORMAL);
  Application.Terminate;
end;

This procedure is supposed to restart the application. I am certain that the deleting problem is caused by the quick start of the second application, because if I restart it myself, giving it a little time, the files get deleted normally.

tl;dr version: I need to call ShellExecute() which waits a bit (0.1 sec or so) and THEN executes the command.

Note

I tried using the -ping command to try to delay it, but it didn't work.

Thank you very much in advance

Edit: Rephrased

I need this to happen || First app closes; Wait 100 ms; second app opens ||. I need to call ShellExecute first, then wait until the calling application closes itself completely, then execute the shell (i.e. open second application)