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";
}
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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 ) {
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..to read like this:

for my $k (sort {$a <=> $b } keys %$ref_HoH) {
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Cheers,
Darren :)