This uses a core module (and is Sick And Twisted(TM)):

use strict;
use warnings;

use Math::BigInt;


my $s = 'Hello World';
$s = reverse
  ((Math::BigInt->new('0b' .
                      (unpack('B*', $s) &
                       ('00000000' .
                        ('11111111' x (length($s) - 1))))))->as_bin())
+;

$s =~ s!b0!!;
$s = reverse(pack('b*', $s));
print "'", $s, "'\n";
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