Here's an idea:
Have a simple text file on your server (call it "webmasters.ip"

and in that file, store your ip address. Now, the scripts that increment the counter, will check to see if REMOTE_ADDR is the same as the ip in that file.
OK - no solution yet... I know - the trick is to make a new script that servers not other purpose than to alter that text file to match the $ENV{REMOTE_ADDR} of the current user. you can password protect it if you like - but only the webmaster should be able to access that script. So now, everytime you 'dial up' onto the internet, go to that script first thing - it will alter the "webmasters.ip" file and your server will recognize you from there on out - as long as your ip doesn't change (you have to re-logon for instance...).
An example of the script that alters the webmasters.ip file would be:
#============== MeetNewWebmaster.cgi ===========
use CGI;
use CGI::Carp qw/fatalsToBrowser/;
my $j = new CGI;
print $j->header();
open(FILE, ">path/to/webmasters.ip"

|| die $!;
print FILE $ENV{REMOTE_ADDR};
close(FILE);
print "Greetings new webmaster...<br>\n";
print "New ip address: $ENV{REMOTE_ADDR}<br>\n";
print "You may now peruse the website<br>\n";
print "without being noticed...\n";
#================= END ==========================
And the scripts that test for the IP should check the
webmasters.ip file to test against the $ENV{REMOTE_ADDR} and act based on that.
--jim