There's lots of discussion below that is interesting, but I'm guessing it's also pretty deep for (what seems to me) a relative "perl newbie" poster ...

Efficiency aside (and in the spirit of 'how the hell do I get this to work'), why not use:

@files = sort { lc $a cmp lc $b } @files;
[download]

???

And as you build your perl skills, revisit the efficiencies of your code.