Ye, it looks awkward or longer, because Perl have no such array index function or sort by array index function in its core.

Perl has some string index functions (index and rindex). In your example they may be used instead of hash, e.g. using Schwartzian transform:

  my $i = 0;
# use constant PCHR => split //, 'KQRBNP';
# my %pchr = map { $_ => $i++ } PCHR;
  use constant PCHR => 'KQRBNP';
  my $w1 = 'QRKPNB';
  my $w2 = join '', 
    map $_->[1],
    sort { $a->[0] <=> $b->[0] } 
    map [ ( index PCHR, $_ ), $_ ],
    split //, $w1;
  print "$w1 -> $w2\n";
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I'm not sure if it looks less awkward ;)