As I understand, you are looking for a script hook to use after statistics processing. There are no script hooks available for this due to the nature of how statistics are processed. You can find a full list of available script hooks at:
I'm using a Nginx web server as a front-end to Apache, and every time, after web logs are processing, nginx is unable to write logs to files, and I must send a special signal to nginx worker process to reopen all log files...
You could configure specific times for statistics to process via:
"WHM >> Server Configuration >> Statistics Software Configuration >> Configure Statistics Process Time Schedule"
Then, you could add a cron job to run at specific times to execute the required commands. The use of Nginx is not supported by cPanel, thus there are no native tools available with cPanel to resolve this type of issue.