Expanding on Hena's idea I wonder if it would be even more efficient to use Tie::File to go through, writing replacements as you go (untested):

use Tie::File;

my $inputfile = "samplein.txt";
&replacer($inputfile);

sub replacer {
   tie my @currentfile, 'Tie::File', $inputfile or die "$!";
      my $inputline;
      foreach $inputline ( $currentfile[0] .. $#currentfile ) {
         foreach my $key (keys %regex) {
            $inputline =~ s/$key/$regex{$key}/gee;
         }
      }
   untie @currentfile;
}

## Totally untested
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Seems like the write operation would be faster with Tie::File