Let me get this straight, Leonidas are educated in many field, military tactics is just something that is taught on Spartan as education curriculum with that training. In that mind, he has trained enough to use any type of weaponry, so aside from cudgel, I think his ace will be the spear.
Remember the way 300 Spartans rear guard really stopped more than 300.000 Persian because of geographical advantages Leonidas saw over that. Without the rear guards sacrifice I think Persian would decimate Greece.