This is actually a nice approach, especially since it automatically deals with the other edge condition mentioned by ysth below, as well as the one cited in the OP.

But I think you missed some of the details -- the monk only wants to put in asterisks for certain paramters in the string:

sub obscure {
   my ($self, $s) = @_;

   my %tags = qw/fred x wilbur x/;

   return join '&',
        map { my ($n,$v) = split /=/; 
              ( exists( %tags{$n} )) ? "$n=".'*' x length($v) : $_ }
        split /\&/, $s;
}
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(Sorry, but I didn't see the relevance/need for "use constant" there, so I left it out.)

(updated to fix indentation in the code)