That's cheating a bit, because it only works with arrays of nonnegative integers. The OP version works with any numeric elements (<=> comparison). Interesting angle nonetheless.

The hashless solution doesn't actually need any sorting. The following is a brute force filter, which maintains the input order of elements:

use v5.14;
use warnings;

sub uniq {
    my @u;

    for my $x (@_) {
        next if grep { $x == $_ } @u;
        push @u, $x;
    }

    return @u;
}

say join ', ', uniq(29,24,0,24,24,12,0,10,10,19,17,15,13,1,12,12,24);
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It's of course asymptotically slower than sorting (O(n**2) vs O(n*log(n))), but if the input happens to be mostly duplicates, it will be faster in practice.