larry_bar56- Welcome to Autopia! If you wash your car with Dawn, it'll strip off most of the wax. But, even your fresh coat of wax won't stand up too well to the abrasives required to remove swirls. If it'll remove PAINT (swirl removal) it'll easily remove the wax too. It MIGHT gum up your applicator/pad a bit, but it shouldn't be a real problem. I myself would probably wait until the wax shows signs of degrading before doing anything, unless the swirls are SO bad that the car looks crappy.
Generally, what bretfraz said
Remove the swirls, and use the proper wash/dry techniques to avoid introducing new ones.
I recently used the PI-II rubbing compound (I think the p/n is 39002) and I DO think it might be just the thing for your application, followed by the SMR. Don't be nervous about the "rubbing compound", it's much milder than I thought it would be (not like the semi-liquid-sandpaper paste stuff). I wouldn't use it all the time, or press real hard, but it's really not all that aggressive.
BTW, if you decide to spring for a PC, your white car can be a breeze to keep nice. Without one, you'll just have to work a little harder.