Well, I get it to almost the same speed as the double reverse, but only after some modification:

#!/usr/bin/perl

use strict;
use warnings;

use Benchmark qw /cmpthese/;

chomp (our @strings = <DATA>);

our (@a, @b, @c, @d);

cmpthese -1 => {
    juerd  => '@a = map {scalar reverse ucfirst lc reverse} @strings',
    davido => '@b = map {my $t = $_; $t =~ s/^(.*)(.)$/\L$1\U$2/; $t} 
+@strings',
    dada1  => '@c = map {lc (substr ($_,  0, length ($string) - 1)) .
                         uc (substr ($_, -1, 1))} @strings',
    dada2  => '@d = map {lc (substr ($_,  0, -1)) .
                         uc (substr ($_, -1,  1))} @strings',
};


die 1 unless "@a" eq "@b";
die 2 unless "@a" eq "@c";
die 3 unless "@a" eq "@d";

__DATA__
ACta
abcdefghijklmnopqrstuvwxyz
abcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz abcdefghijklmnop
+qrstuvwxyz
I have a question!
yet another way, which should be quickier than the double reverse:




          Rate davido  dada1  dada2  juerd
davido 21081/s     --   -68%   -70%   -70%
dada1  65511/s   211%     --    -6%    -7%
dada2  69592/s   230%     6%     --    -1%
juerd  70275/s   233%     7%     1%     --
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Abigail