Ok, that changes things somewhat. How about this:

#!/usr/bin/perl
use warnings;
use strict;

my $str1 = <<STR;
col1    col2    col3
1    4    7
2    5    8
3    6    9
STR
my $str2 = <<STR;
col1    col2    col3
1    44    77
2    55    88
3    66    99
STR

open my $fIn, '<', \$str1;

my $index = 0;
my %fileCols = map{+"file1 $_" => $index++} split /\s+/, <$fIn>;
my @file1Data;

push @file1Data, [split /\s+/] while <$fIn>;
close $fIn;

my @wantedCols = ('col1', 'col3', 'file1 col3');

open $fIn, '<', \$str2;
$index = @{$file1Data[0]};
$fileCols{$_} = $index++ for split /\s+/, <$fIn>;

my @slice = map{exists $fileCols{$_} ? $fileCols{$_} : ()} @wantedCols
+;

print join(' ', map{(split /\s+/)[-1]} @wantedCols), "\n";
while (<$fIn>) {
    chomp;
    print join (' ', (@{$file1Data[$. - 2]}, split /\s+/)[@slice]), "\
+n";
}
[download]

Prints:

col1 col3 col3
1 77 7
2 88 8
3 99 9
[download]

Note that effectively all of the first file is read into memory to avoid having to re-read and parse it for each following file. This is fine so long as the first file is less than about half the memory you have available.