I don't understand the purpose of what you're doing, but you can move some of the work outside the main loop like this:

my @pat;
foreach my $r (@seq) {
   my $t = $r;
   $t =~ s/\h+/bbb/g;
   push @pat, [ $r, $t ];
}
while (<$fh>) {
   foreach my $p (@pat) {
      s/$p->[0]/$p->[1]/g;
   }
   print Newfile;
}
[download]

And if you want to get fancy, maybe even this:

my $seq = join '|', @seq;
my %seq;
foreach my $r (@seq) {
   (my $t = $r) =~ s/\h+/bbb/g;
   $seq{$r} = $t;
}
while (<$fh>) {
   s/($seq)/$seq{$1}/go;
   print Newfile;
}
[download]