# Make walk() return a list and collect the results:
sub walk {
    my ($i) = @_;
    my @local_results = $i;
    for (@{$hash{$i}}) {
        push @local_results, walk($_);
    };
    return @local_results;
};

...

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