You are actually required by law to have a reservation. The only cab services that are allowed to pick you up without a reservation are licensed taxis ("black cabs" in London, even though they're not always black) which operate from the official taxi rank. Beyond these two categories, everyone else touting for business is illegal, unlicensed, likely to be uninsured, and possibly on the lookout for easy pickings.
These car services do thousands of these pickups every day, only a small proportion of which will be cruise ship passengers. As long as they have your flight number, they'll keep on top of what's happening, and they are operationally flexible so they can adjust if need be.
But it will be useful to have a working phone on you when you arrive, so that you can talk directly to the driver if you need to. IME, the drivers for the car service that I use usually try to keep track of your timing and whereabouts by phone rather than relying on a sign. At any one time there can be dozens if not over a hundred drivers waiting outside the exit from customs, each holding a sign - good luck with your speed reading! (And no, I don't usually plug the service that I normally use because in general, all of the usual suspects are much of a muchness.)