I was always told to try to eat a little bit of something if I was ever sick and if I couldn't then some kind of sugary drink would also help. I don't think it'll necessarily do much harm if you skip one meal, as long as you're checking your sugars and ketones and drinking plenty of water to make sure everything is ok on the diabetes side of things.
If it were me I would try to eat a little bit of something like a plain piece of toast, plain crackers, banana, soup etc, even if it is a small amount. Your body needs energy to be able to fight the illness and food will help with that. I Hope you feel better soon!