If you don't want to do an internal redirect (or aren't using Apache) then you can just set the MIME type and output a small image file. (A 1x1 transparent GIF is a good idea.)

#!/usr/bin/perl

use strict;
use warnings;

use CGI;

# do statistics stuff...

my $q = CGI->new;
print $q->header( 'image/gif' );

# slurp file and output
local $/;
open my $fh, 'tiny_img.gif' or die $!;
print <$fh>;
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