I have just quickly misted it with a bit of Windex, and has not seemed to do any harm. This said, seems I may have read a caution against using glass cleaner? Have you noticed the post re glass protective covers which are available?
I would recommend a screen protector. I added one on my 1958. There’s a thread on it. The one I installed was “oil phobic” and does seem to pick up less smudges. Wipes clean with a slightly damp high quality microfiber.