If the swirls are quite light, you could try using Dodo Juice Lime Prime, which is a pre-wax cleanser that contains micro-abrasives so has slight "cut" properties, which will help to remove the swirls. You can apply this by hand or machine, whichever you prefer, and it will leave the paintwork in perfect condition for carnauba wax to be applied over the top, as the pre-wax cleanser is designed to enable the wax to bond with the paint.
As Jules said... if you want to achieve as close to 100% correction as possible, you'd more than likely need to look at a machine correction stage
Hope this helps
Taryn and Jim