I have resolved the issue. This was achieved simpling by adding use Email::Sender::Transport::Sendmail; to the beginning of the script. The documentation made me believe that this was optional (possibly on a different system it would be, but evidently Email::Sender was having trouble figuring out a default way to send mail on my system, for whatever reason). Still not sure about the root causes, but happy that it's working :)

To briefly answer your questions: yes, sendmail was installed and functioning correctly. I was not planning to use an SMTP server.