Not really, no. You could look up the mtime directly in the sort callback (see perldoc -f sort), but stat()ing files is an expensive operation and sort tends to take N*log(N) iterations, so you'd be doing too much work that way. The only way to do this efficiently would be to look the mtimes up first in a single pass. That could be done using the Schwartzian Transform.

my @dirfiles =
    map $_->[0],
    sort { $a->[1] <=> $b->[1] }
    map [ $_, +(stat "$dirname/$_")[9] ],
    grep $_ ne '.' and $_ ne '..',
    readdir ORDERS;
[download]

Note that using a regex to filter out the . and .. here is overkill and even results in unexpected behaviour: the $ matches in front of a \n so the regex will also throw away files called ".\n" or "..\n".

Update: changed stat $_ (d'oh) into stat "$dirname/$_"

Makeshifts last the longest.