Even sorting the keys of a normal hash by value¹ can only be done by somehow tunneling the reference into byvalue() by closure/currying (like choroba showed) or by doing a (schwarzian?) transform of the hash into an array of key/value-tupels.

Both approaches look like overkill if you can do this straightforwardly:

my %h    = %{$self->{hash_ref}};
my @keys = sort { $h{$a} <=> $h{$b} } keys %h;
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Easy to read, easy to understand.

So why ?

  DB<100> $self={
           hash_ref=>{item1=>'value1',item2=>'value2'}
           }
 => { hash_ref => { item1 => "value1", item2 => "value2" } }

  DB<101> %h=%{$self->{hash_ref}}
 => ("item1", "value1", "item2", "value2")

  DB<103> @keys=sort {$h{$a}<=>$h{$b}} keys %h;
 => ("item1", "item2")
[download]

PS: downvoted for lack of indentation, I agree with the Guido comment.

¹) hint "Reduction to a simpler problem"!