Well, I'm not sure I'd do this, but if you TRUST YOUR USER, you can do:

while (<FILE1>) {
  do $regex_file;
  print;
}
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where $regex_file holds the filename to execute. It's scary though, because the user could put ANYTHING in that file. So maybe you want a sandbox, via Safe:

use Safe;
use strict;
use warnings;

# read the regex file into $code
my $code = do {
  local $/;
  open my($rx), $regex_file;
  <$rx>;
};

# create a sandbox
my $sandbox = Safe->new;

# allow acceptable operators (perldoc Opcode)
$sandbox->permit_only(qw( :base_core :base_orig ));

while (<FILE>) {
  $sandbox->reval($code);
  print;
}
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Try that out.