不包含执行php文件:shell_exec()已被禁用

I need to make use of the PHP function shell_exec(). Unfortunately I'm using shared hosting and shell_exec() has been disabled for security reasons.

With the cron job php -q /home/user_name/exec_test.php >/dev/null 2>&1 I found out, shell_exec() is only disabled in /home/user_name/public_html/ but not in /home/user_name/, which I can access via cron job.

Of course, I cannot access the directory /home/user_name/ via browser. (I would prefer not to use cron job.)

My idea was to include (include "/home/user_name/exec_test.php";) my exec file from a php script in the browser accessible direction. Unfortunately this gives me the same error: shell_exec() has been disabled for security reasons

Is there a way I can reach what I want? Is there a way to execute /home/user_name/exec_test.php without include it in /home/user_name/public_html/ directory?