I think the following will do the trick:

my @chars = map quotemeta,
            split //,
            $word;

my $re = join '|',
         map { local @_ = @chars;
               $_[$_] = '.';
               join '', @_
             }
         0..$#chars;
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Using Regexp::Assemble should be faster:

use Regexp::Assemble qw( );

my @chars = map quotemeta,
            split //,
            $word;

my $ra = Regexp::Assemble->new();

for (0..$#chars) {
   local @_ = @chars;
   $_[$_] = '.';
   $ra->add(join '', @_)
}

my $re = $ra->re();
[download]

Generalizing this approach for Hamming distance > 1, using the combinations iterator from Iterating over combinations:

sub gen_regex {
    my ($target, $n) = @_;

    my @chars = split //, $target;
    my $ra    = Regexp::Assemble->new();
    my $iter  = combinations( $n => [ 0 .. $#chars ] );

    while (my @c = $iter->()) {
       local @_ = @chars; 
       $_[$_] = '.' for @c;
       $ra->add( join '', @_ );
    }

    $ra->re();
}
[download]

blokhead