Really short hair should use slim plates. There are some that are about 3/4 of an inch so they're great for short hair. As a tip, choose ceramic or tourmaline plates (or both!) . Titanium would get way to hot and to have so much heat near your scalp would just be a bad idea. You could even check out some men's hair straighteners, those are designed for super short hair.
Some brands give you a glove but you can always buy one separately.