Which might be something along the lines of:

my $flag = 0 ;
my $scaffold ;
my $enumerator ;

while (my $fastaline=<FILE>) {
  if ($fastaline=~ m/^>(\S*)/) {
    $scaffold   = $1 ;
    $enumerator = 1 ;
    $flag       = 1 ;
  }
  elsif ($fastaline =~ m/[ACGT]/) {
    if ($flag) {
      print WORKFILE ">$scaffold.$enumerator\n" ;
      $enumerator++ ;
      $flag = 0 ;
    } ;  
    print WORKFILE $fastaline ;
  }
  else {
    $flag = 1 ;
  } ;
} ;
[download]

NB: this is not checking that the input is well formed: (a) it accepts any line that contains at least one [ACGT] as being a line to keep; (b) it does not check that the lines being dropped are all N; (c) it does not check the exact form of >scaffold lines; (d) it does not check that at least one ACGT line follows each >scaffold line; ... If the input is 100% trusted, that's fine... (if 100% trustworthy input isn't an oxymoron).