Hey,
This seems quite straight-forward. I just need to know, does your hosting service provide any SSH access? There should be an option within the cPanel to enable this. If so, I can set this up for you pretty quickly.
If it does have SSH, every time you wish to run the script on the server, you can simply open an SSH client such as PuTTy and instantly begin running the script on the server. Just as you would on a local Linux terminal.