After hours of trying, I still wasn't able to get it working.
So time for an ugly bypass solution. Instead of a python script, I made a php script to do the work>
And run this cron job 'php /home2/******/public_html/Test/cron.php' and it works.
But I still want to know how to get the mysql.connector to work via crontab ;-)
on my hosting provider, I try to make a cron job running a .py-file.
The cron-job starts but I always get this error message "ImportError: No module named mysql.connector".
When I run exactly the same script via CLI, it runs smoothly. It connects to my db, it updates, inserts, ...  So, there is no issue with having this module (yes I installed).
So, how can I get this cron job to work?
This is how I start that job: python /home2/******/public_html/Test/cron_job_test.py
(when I run this via CLI it works)
Many thanks,
Peter
ImportError: No module named mysql.connector when using cron-jb