If you just need to process them in chronological order, you could sort them based on their modification times:

my @files = <*.txt>;

@files = map { $_->[0] }
     sort { $b->[1] <=> $a->[1] }
     map { [ $_, (-M $_) ] } @files;
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Gotta love that Schwartzian Transform.

You'll have to be in the appropriate directory for this to work, and you'll end up with @files containing a the filenames, sorted ascending by last modification time. You could do a simple addition and splice operation to pare down the list to the files you haven't used before.

It's a different approach, anyway.