Is 20 minutes enough time?
Sorry but there is no way to lock specific phone functions. You might go to Precentral and suggest the app to the developers forum. Those guys are amazing, make a suggestion and a week later its done.
Nothing absolutely ensures that your eyes are not hit. There is always some risk that the glasses will fall off or get knocked off, especially because those glasses are held on only by the earpieces. Glasses with an elastic band that goes around the back of your head are much safer.