Here I completely agree that the price is usually much higher at night than during the day. And cab drivers are very quick to realize where the tourists are. What hotel are you staying at? The hotel should not care whether it is day or night, the transfer should always leave. But if there is such a situation, I can leave you the contacts of the service, which I always use when you need to book a transfer from the airport https://gettransfer.com/en/directions/cyprus. On this site you can immediately enter the address where you need to pick you up and where to take you and immediately see the price. I have always had only good experiences with this transfer. The driver met me with a sign, helped me with my suitcases, and we got to the right address without any problems.