You can execute the cron.php file from your Magento root directory.
Before you do that, you may need to disable the following lines in the default Magento .htaccess file:-
<Files cron.php>
#Order allow,deny
#Deny from all
</Files>
This isn't recommended though from a security point of view so you may want to restrict it's access to a specific IP.
I do find it quite odd that your hosting provider isn't able to support Cron Job. Personally I will have doubts on whether they can run your Magento store properly if they do not provide access to one of the most basic requirement like Cron Jobs.