You are over-complicating things.
To print the keys of your hash, sorted numerically - all you need to do is: 
for (sort {$a <=> $b} keys %foo) {
    print "$_\n";
}

[download]

Update: - to more directly answer your question, you need to change this line: 

for my $k ( sort {%{ $ref_HoH{$a} } <=> %{ $ref_HoH{$b} }    }keys %$r
+ef_HoH ) {

[download]
..to read like this: 
for my $k (sort {$a <=> $b } keys %$ref_HoH) {

[download]

Cheers,
Darren :)

In reply to Re: Sorting a Hash of Hashes by McDarren
in thread Sorting a Hash of Hashes by Anonymous Monk

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