I think that you will have to write a wrapper application that reads the executable output line by line and writes that output into a different logfile - as long as you can make the external application write everything to stdout/stderr, this should be possible. I don't have the time to create a working script, but here are some simple cases that could work (depending on the application) :

  open APP, 'application.exe |' or die "Uhoh : $!";
  while (<APP>) {
    my $filename = get_logfilename_of_today;
    open LOG, "<", $filename;
    print LOG $_;
    close LOG;
  };
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The above part only works if the application does not write to STDERR. perldoc perlipc suggests the following snipped if you need to read and write :

    use FileHandle;
    use IPC::Open2;
    $pid = open2(*Reader, *Writer, "cat -u -n" );
    print Writer "stuff\n";
    $got = <Reader>;
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If you need to read and write, also take a look at IO::Select.

perl -MHTTP::Daemon -MHTTP::Response -MLWP::Simple -e ' ;    # The  
$d = new HTTP::Daemon and fork and getprint $d->url and exit;#spider
($c = $d->accept())->get_request(); $c->send_response( new   #in the
HTTP::Response(200,$_,$_,qq(Just another Perl hacker\n))); ' #  web
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