There is perhaps just one slight problem with using Perl for this at all. If you do not have access to cron, I take it that you do not have root access. In this case, I will also assume that you have an account on someone else's remote machine.

With these assumptions, this means that you would have to keep a telnet or ssh session open to the remote server in order to keep the Perl script running. As many people will find, telnet and/or ssh are not the best ways to keep a persistent connection: especially telnet sessions have a tendency to hang at unexpected moments. In this case, if it happens to hang while the script is running, the execution of the script would be terminated, resulting in no crontab running.

Just my 10 cents (yes, the price of opinions has been increased by 8 cents)