# Make walk() augment the result list:
sub walk {
    my ($i,$results) = @_;
    # If we're called with just one argument, we need to return a fresh list
    $results ||= [];
    push @$results, $i;
    for (@{$hash{$i}}) {
        walk($_,$results); # here, we don't care about the results of walk()
    };
    return @$results;
};

...

foreach my $r (@array) {
    my @big = walk($r);
    ...
};