Here's how I would write it, compromising between brevity and readability. (untested)

#!/usr/bin/perl
use strict;
use warnings;

my $dir = "/home/my/files" ;
chdir $dir or die "$!";
opendir(DIR,$dir ) or die "$!";
my $i = 1;

for (grep { !/^\./ } readdir(DIR)) {
    rename $_,sprintf ('%03d-%s',$i++,$_) or warn "Couldn't rename $_:
+ $!";
}
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I think you may be trying too hard to use perlisms (like the regexp replace). Often, it's better to just look for simpler ways to do things.