No, you should not eat watermelon after its use-by date.
Use-by dates are specifically about food safety. Eating food past its use-by date, even if it appears and smells normal, can be dangerous and could make you very ill. This is because the food may contain harmful bacteria that can grow to unsafe levels even without noticeable changes in the food's appearance or odor. While a watermelon might seem fine, consuming it after the use-by date carries a risk of foodborne illness.
