L.'s husband, here.
I worked at a audio-visual contractor for three years. Here are a couple tips:
Do NOT spray directly on the screen. The liquid can drip and once it makes it past the edge of the frame you can be in big trouble. Spray a little cleaner on a lint-free rag or high-quality paper towel, making it slightly damp. You should not have any liquid left on the screen after two passes on the rag. Also, there is a company named, "Monster Cable." They make a great cleaning set for this very purpose. If this is something you do frequently, I recommend it.
Here's the webpage for it through Target. Good luck.
http://www.target.com/Monster-Cable-3-pc-Screen-Cleaning/...