A Schwartzian Transform may do the trick. You need to sort the values, which would be:

my @values = sort { $a <=> $b } values %hash;

... but you need to keep track of the keys as well. You can build a temporary data structure of pairs, or a list of two-element array references, where the first element is the value and the second element is the key:

my @pairs = map { [ $hash{$_}, $_ ] } keys %hash;

To get back the keys, you need to map over this list and extract the second element of each pair:

my @keys = map { $_->[1] } @pairs;

That looks like a lot of useless work, and it would be, except that you can stick as many list-transforming functions in the middle as you want -- including a sort. You can also drop the temporary arrays; they're unnecessary. The result is:

my @keys_sorted_by_value =
    map  { $_->[1] }
    sort { $a->[0] <=> $b->[0] }
    map { $hash{$_}, $_ }
    keys %hash;
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Update: Fixed a typo found by Roy Johnson.