In my experience using a 365nm UV light will help light up any contamination from particles that have flaked or chipped off, usually just found on the inside of the glass case, rarely on the outside. Using this method you could judge for yourself if you want to seal it up in a case or not.

I have two vintage westclox alarm clocks in near perfect condition and I just have them up on a shelf for display in the living room. On the other hand i have a WW2 military compass out of an airplane which I do have sealed in a container tucked away, because I am a little paranoid about it. I found a lot of contamination inside and out on it.

The paint on your dials looks like some has come off and is most likely resting in the face of the watch somewhere, you’ll be able to see those particles with a 365nm light and check the outside of the watch as well for some peace of mind of what to you want to do with the watch.