Loading 200 MB into available memory is likely possible on today's hardward. If so, the following runs ~ 7 times faster. The idea here is iteratating over seq one time. For larger data files, one can chunk 300 MB at a time time and not forgetting to read till the end of line to have a complete chunk. Then process the chunk similarly.

use strict;
use warnings;
use autodie;

open Newfile, ">", "./Newfile.txt" or die "Cannot create Newfile.txt";

my ($f1, $f2, @seq) = ('seq.txt', 'mytext.txt');

open(my $fh, $f1);
foreach (<$fh>) {
  chomp; s/^\s+|\s+$//g;
  push @seq, $_;
}
close $fh;

@seq = sort bylen @seq;  # need to sort @seq by length.

my $data; { open($fh, $f2); local $/; $data = <$fh>; }

foreach my $r (@seq) {
  my $t = $r; $t =~ s/\h+/bbb/g;
  $data =~ s/$r/$t/g;
}

print Newfile $data;
close Newfile ;

exit 0;

sub bylen {
  length($b) <=> length($a);
}
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