Is there a way for my script to know which "mailing" system is on a server?

The best way to find out is to contact your system administrator. Just the fact that there is a /usr/bin/sendmail doesn't mean that it's useable - if there is no correct sendmail configuration file, mail may not work, or not work corrrectly. It also might not be the correct sendmail, some systems have it in /usr/lib or /usr/sbin.

Abigail