Physical Danger
There isn't a whole lot of physical danger to worry about as an orthoptist. Your exams don't hurt the way some doctors (read: dentists) often do, and you don't work around hazardous fluids or materials. You do work with body parts, however, so make sure you use the proper precautions (i.e. gloves, soap). You're not an opthamalogist, so you don't have to worry too much about dealing with disease of the eyes, but it never hurts to be cautious.
Gooey eyes aside, the most you have to worry about is tripping over something, or falling asleep in a darkened examination room while working with a client. Trust us, the old line about checking the inside of your eyelids won't work if you get caught. Ultimately, your eyes may feel strained by the end of the day, your feet may ache, and you may have talked yourself hoarse at the close of a busy shift, but you won't be put in harm's way.