Depending upon your data, simply checking first that the strings don't match can make it much faster :

sub hd1
{
     #String length is assumed to be equal
     my ($k,$l) = @_;
     # next line added
     return 0 if $k eq $l; 
     
     my $len = length ($k);
     my $num_mismatch = 0;

     for (my $i=0; $i<$len; $i++)
     {
      ++$num_mismatch if substr($k, $i, 1) ne substr($l, $i, 1);
     }

     return $num_mismatch;
}
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