I'm sure there will be enough places open. It'll just be a bit more like the end of September. Places like Tasty Corner, Yiannis Grill, Yiannis, Town Pizza, probably Beachcomber, are small family-run businesses which don't have the high staff requirements of the hotels, so they can work all right with lower customer levels, and there's less competition. I expect that Mango, Havana and Manthos will be open to provide for the beach. Mistral's more doubtful, because they mostly come from Sidari. Lesley will be able to report on Vicky, and I expect Barras will be open, and Waves.
So I wouldn't worry too much. There won't be millions of sunbeds on the beach, which I happen to think is a good thing!