Since you're transforming anyway, might as well put it in a more easily sortable format! 
   map  { $_->[0] }
   sort { $a->[1] cmp $b->[1] }
   map  { my ($m, $d, $y) = m{(\d\d)/(\d\d)/(\d\d)};
          $y += y >= $cutoff ? 1900 : 2000;
          [ $_, sprintf('%04d/%02d/%02d', $y, $m, $d) ]
        }

[download]

Or for extra speed, avoid creating all those arrays and references. 

   map  { substr($_, 10) }
   sort
   map  { my ($m, $d, $y) = m{(\d\d)/(\d\d)/(\d\d)};
          $y += $y >= $cutoff ? 1900 : 2000;
          sprintf('%04d/%02d/%02d', $y, $m, $d) . $_
        }

[download]

Update: Added missing $.

In reply to Re^2: Combining s/// by ikegami
in thread Combining s/// by kangaroobin

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