Good move - that modification convinces me. Although in that case, the underlying algorithm we now have seems too simple to bother with the overheads of a heap module (update: because a hash is a special sort of heap!). The following algorithm uses the bare bones to deliver the top-n into %SortaHeapy, without using any sorting (code updated):

$NumOfPortsToGet = 10;
local $loaded = 0;
my %SortaHeapy = ();
for my $key ( keys %Stats ) {
    ($key eq "UnauthOrigin") or SortaHeapy( $key );
}

sub SortaHeapy{
    my $key = shift;
    # if mini-heap not full just load it in
    if ( $loaded < $NumOfPortsToGet ) {
        $SortAHeapy{ $key } = $Stats{ $key };
        $loaded++
        return;
    }

    # otherwise do the degenerate heap sort/replace
    for my $hkey ( keys %SortaHeapy ) {
        if ( $SortaHeapy{ $hkey } < $Stats{ $key } ) {
            delete $SortaHeapy{ $hkey }; # replace
            SortaHeapy{ $hkey }; # but iterate the victim
            return
        }
    }
}
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