Don't ya just hate them Grrr
A 200mw green laser is dangerous to use without good laser safety practices! You should never point the laser near your eye and be mindful of reflections. I work in a laser lab and I would never work with a 200mw laser without safety goggles. Get goggles. You are correct to be concerned about the IR as well. The green laser is actually an infrared laser (1064nm) that has a special material to converted the output to green (532nm). However, some of the IR will leak out as well if the manufacturer did not put an IR filter in to block it. If the laser starts to fail in the future, it could start to put out a LOT of IR as it does not properly convert to green. This IR is especially dangerous because you can not see it, but it will focus on your retina and cause damage. One way to tell if there is IR leakage is to shine the beam through a prism. This would split the green and IR beams in different directions. The prism disperses light, like a rainbow, with the infrared red side of the rainbow, but you won't see it with your eye. Then, you need to find a way to detect the IR light, with some sort of photodiode or light detector.
Did you ask?YOu did not say where you are from (USA?) but in the US the schools must meet the local fire codes. You may have a sprinkler system overhead which obviates the placement of individual extinguishers. The new style of sprinklers are flush mounted with only a small circular plate showing in the ceiling.. not the old style brass fittings that hang down.