The question is if you want it fast or pretty.

Without extra modules, this doesn't look particular awkward to me.

use strict;
use warnings;

my $PCHR = "KQRBNP";
my $w1   = "QRKPNB";
my $w2 =
  join "",
  sort { index ($PCHR, $a) <=> index ($PCHR, $b) }
  split //, $w1;

print "$w1 -> $w2";
[download]

of course it's far more efficient to store the index in a hash, which in turn needs to be precalculated.

Others have shown you external "sort_by" implementations using so-called "key-functions" like in Python ( That's when you can avoid to repeat code for $a and $b).

But I'm not sure if these key-functions - in Python or CPAN - actually cache the results for performance optimization in a hash. (This might be too clever if a key function is supposed to vary results)

Which brings us back to the question: fast or pretty?