when waxing the car must be operating room clean as the swirls are caused by fine dust or the dirt in a film on the car not easily removed. The fastest wat to remove them is with a buffer. USe a cleaner first and then switch the pad and use a polish and then switch the pad and use a high quality wax.
You can do the same by hand, Buy a minimum of a dozen white cotton covered foam pads and turn them over as soon as the slightest sign of dirt. You will proably go through at least 6 to 10 with the cleaner, another 4 to six with the polish and 2 to four with the wax. I usually do my car by hand and I wast the pads and use them again for the cleaner and polish. Only new ones for the wax.