Note 1:
$a <=> $b compares numerically.
@a = sort { $a <=> $b } (1, 5, 3);
$a cmp $b compares alphabetically.
@a = sort { $a cmp $b } qw(apple orange banana);

Note 2: readdir's outputs doesn't need to be chomped.

This will do the trick:

@status = sort {
   my $mtime_a = (stat("$target_dir\\$a"))[9];
   my $mtime_b = (stat("$target_dir\\$b"))[9];
   $mtime_a <=> $mtime_b
} @status;
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But it's very expensive because stat can be called multiple times for each file. So here's the workaround (called the Schwartzian Transform):

@status = (
   map  { $_->[0] }
   sort { $a->[1] <=> $b->[1] }
   map  { [ $_, stat("$target_dir\\$_"))[9] ] }
   @status
);
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