Could you use : wget -O /dev/null -o /dev/null example.com

What I can see on the other server fault forum it says. “Here -O sends the downloaded file to /dev/null and -o logs to /dev/null instead of stderr. That way redirection is not needed at all.”

and the other solution is: wget -q --spider mysite.com

refer : https://serverfault.com/questions/619542/piping-wget-output-to-dev-null-in-cron/619546#619546