Therefore, if I really want to sort on the hash values, it would make sense to create a new temporary hash in which the values and keys are swapped, and then sort that new array on its keys (which are the values of the original hash), rather than the values. Is that incorrect?

The answer, as usual, is "it depends". Of course extra hash lookups will slow things down, but by how much? Also (and this is where the "it depends" kicks in), in general you also have to factor in the time it'll take to construct a reverse hash.

Here is a very simple test:

#!/usr/bin/perl

use strict;
use warnings;
use feature qw/say/;
use Benchmark qw/cmpthese/;

srand 0;
our %hash = map { rand() } 1..1000;

my $regular = sub {
    sort { $hash{$a} <=> $hash{$b} } keys %hash;
};

my $keysonly = sub {
    sort { $a <=> $b } keys %hash;
};

my $reverse_noref = sub {
    my %reverse_hash = ();
    foreach my $key (keys %hash) {
        $reverse_hash{$hash{$key}} = $key;
    }
    sort { $a <=> $b } keys %reverse_hash;
};

my $reverse = sub {
    my %reverse_hash = ();
    foreach my $key (keys %hash) {
        push @{ $reverse_hash{$hash{$key}} }, $key;
    }
    sort { $a <=> $b } keys %reverse_hash;
};

cmpthese(-2, {
    regular       => $regular,
    keysonly      => $keysonly,
    reverse       => $reverse,
    reverse_noref => $reverse_noref
});
[download]

On the machine I'm currently on, this produces:

$ perl 1099601.pl
                 Rate       reverse reverse_noref       regular      k
+eysonly
reverse        2222/s            --          -35%          -93%       
+   -93%
reverse_noref  3406/s           53%            --          -89%       
+   -89%
regular       31693/s         1326%          830%            --       
+    -0%
keysonly      31726/s         1328%          831%            0%       
+     --
$
[download]

So in isolation, the difference between "regular" (with the hash lookup) and "keysonly" (without) is negligible (though of course the latter is ever so slightly faster), while constructing a reverse hash first is 13 times slower. Pushing to an array if/when you can't guarantee values are unique punishes you further, but even without that (reverse_noref) you're still an order of magnitude slower.

What does that mean for you? If you construct a "reverse" hash as you go along, just like you'd construct a regular hash, there may not be much of a difference (or there may be; you'll have to check). If you already have a "regular" hash, just let sort do whatever it needs to do; the difference won't be as big if you only need to construct the reverse hash once and then access it many times, but it'll still be there.

As always, it's better to measure than to assume when it comes to optimization. It may well be that your approach is actually faster for your script and data, and if speed is crucial, then using a less "natural" approach that's faster is entirely fair.