Searching through the forum it seems that no one spotted this way before...otherwise, sorry!
The main point is that since I don't have access on cron and I'm not so comfortable with the "click-the-page-to-fire-the-scrip" thing (yes, I'm never sure that someone will click my website!), I use an external server's test website to fire the script every day at the same hour.
There are many sites that provide this kind of service; personally I use externaltest.com (hey, it's free).
Once signed up you can build a new test (HTTP performance type), give a full path pointing to the script (as http://www.mydomain/phpjobscheduler/firepjs.php
) and everything is done! Every half-hour, every hour or once a day starting from test's registration time the website will trigger the script for you.
I use it on a daily base with the default phpJobScheduler 60 min time frame window and works like a charm.
Thanks a lot to Mr. Walker for this great piece of software!