That seems mostly like the way to do it. Here are some minor improvements:

sub SortArrayOfHashes
{
    my $av= shift;
    my @sum= map {
        my $sum = 0;
        $sum += $_ foreach values %$_;
        $sum;
    } @$av;
    my @idx= sort { $sum[$a] <=> $sum[$b] } 0..$#sum;
    return @{$av}[@idx];
}
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You could also do a Schwartzian Transform, but that would make it slower (though a bit spiffier).

Note that my version avoids copying the values so it might be possible to modify elements of the original array by modifying elements of the sorted array.

        - tye (but my friends call me "Tye")