Using the default sort handler should be even faster:

my @sorted_list = map { substr($_, 23) }
                  sort
                  map { substr($_, 15, 23) . $_ }
                  @file_list;
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Same thing, but uses very little overhead memory:

my @sorted_list = @file_list;
$_ = substr($_, 15, 23) . $_ for @sorted_list;
@sorted_list = sort @sorted_list;
$_ = substr($_, 23) for @sorted_list;
[download]