Does it buy anything to create a hash with keys of some known hash function, and values as indexes pointing into an array? There's one more lookup, but into an array, which should be much cheaper than another hash lookup.

#!/usr/bin/env perl

use strict;
use warnings;

use Devel::Size qw(size total_size);

my $num = 0;
my %hashed_keys;
my @values = ();

for my $word ('aaaa'..'zzzz') {
    # Store $word -> $num
    my $hash_word = some_hash($word);
    my $hash_word_index = scalar @values;
    $hashed_keys{$hash_word} = $hash_word_index;
    push @values, $num;

    # Store $num -> $word
    my $hash_num = some_hash($num);
    my $hash_num_index = scalar @values;
    $hashed_keys{$hash_num} = $hash_num_index;
    push @values, $word;

    ++$num;
}

sub some_hash {
    return shift;
}

my $total_size;
for my $var (\%hashed_keys, \@values) {
    my $tsize = total_size($var);
    printf "%s\n", total_size($var);
    $total_size += $tsize;
}

print "total: $total_size\n";

exit;
[download]

Without a real hash function, this gives:

43383174
29785044
total: 73168218
[download]

...which is only slightly smaller than your original 2-hash result. Mind you, I'm on a 32-bit perl, so that could be the difference.

(Caveats: I've not used a real hash function. I've not accounted for hash collisions.)