my $ignore = '(^The )|(^A )';
...
@sorted = sort { 
    $a =~ s/$ignore//;
    $b =~ s/$ignore//;
    lc( $a ) cmp lc( $b );
  } @indata;

##</code><code>##

%data = map { my $data = $_; s/$ignore//; ($_, $data } @indata;

@sorted = @data{ sort{ lc( $a) cmp lc( $b)} keys %data };