my @list = map BLOCK LIST;
[download]

can be written as

my @list;
for (LIST) {
   push @list, do BLOCK;
}
[download]

So

    my @files =
      map { "$self->{update_dir}/$_" }
        sort { $a <=> $b }
          grep { /^\d+$/ && $_ <= $id }
            readdir $dir;
[download]

could be written as

    my @files;
    for (
        sort { $a <=> $b }
          grep { /^\d+$/ && $_ <= $id }
            readdir $dir
    ) {
        push @files, "$self->{update_dir}/$_";
    }
[download]

If what you have a problem with is really the chaining of all those functions and not map specifically, just reverse the order and use a temporary array to hold the arguments.

So

    my @files =
      map { "$self->{update_dir}/$_" }
        sort { $a <=> $b }
          grep { /^\d+$/ && $_ <= $id }
            readdir $dir;
[download]

could be written as

    my @temp;
    @temp = readdir $dir;
    @temp = grep { /^\d+$/ && $_ <= $id }    @temp;
    @temp = sort { $a <=> $b }               @temp;
    @temp = map { "$self->{update_dir}/$_" } @temp;
    my @files = @temp;
[download]