You can. I would spray it on a cloth, not directly on the screen. I use it (or Spray-away type glass cleaners) on flat screen TV's and computer monitors.

I saw the reason they don’t recommend it on flat screens is because it strips the antiglare coating off. However, with a TV this old, I’m sure that doesn’t exist on it

From a Sony KV-24FV12 Trinitron operating manual, © 2000:

"Unplug the set from the wall outlet before cleaning or polishing it. Do not use liquid cleaners or aerosol cleaners. Use a cloth lightly dampened with water for cleaning the exterior of the set."

my mother has been doing it for years, and i have been doing it too until I switched to flat panel TV's. Just don't spray Windex directly on the screen in case it spills inside the case and causes damage to the electronics inside.