The fact that you needed to visit each element once is why I think your shuffle-and-shift approach is best, as opposed to the integrated thrust approach which has come up a couple times in this thread. The shuffle out of List:Util will scale the same as your implementation, but will likely have a lower constant and use less memory since it uses map in place of a for loop. I've also gotten admonished on using C-style for loops - maybe swap to for my $i (0 .. $#$arrayref) to reduce the bug risk.

If you do dig the the idea of picking weighted ships in place of the shuffle approach, you can swap it to O(n) (or actually O(n*m^2), where m is # of bins) by sorting and caching bounds, so you don't have to count up each ship. Maybe something like this:

my %shipToActBins = ();
foreach my $ship (@shipsInCombat) {
    # Add ship to initiative hash
    if (not exists $shipToActBins{$ship->{thruster}}) {
        $shipToActBins{$ship->{thruster}} = [];
    }
    push @{$shipToActBins{$ship->{thruster}}}, $ship;
}
my %weights = ();
for (keys %shipToActBins) {
    $weights{$_} = 2 * $_ + 1;
}
SHIP: for (0 .. $#shipsInCombat) {
    my $ship;
    my $sum = 0;
    my @bounds = ();

    for (sort keys %shipToActBins) {
        if (@{$shipToActBins{$_}} == 0) {
            delete ($shipToActBins{$_});
        } else {
            $sum += $weights{$_}*@{$shipToActBins{$_}};
            push @bounds, $sum;
        }
    }
    my $roll = int(rand($sum));

    CHOOSE: for (sort keys %shipToActBins) {
        if ($bounds[0] >= $roll) {
            $roll = int(($bounds[0] - $roll - 1)/$weights{$_});
            $ship = splice(@{$shipToActBins{$_}},$roll,1);
            last CHOOSE;
        } else {
            shift @bounds;
        }
    }
    #...
    #Simulated mayhem
    #...
}
[download]