You can skip the second wash cycle if you want. You can use a MF to remove any residue after claying a section. If any clay residue is left on the paint the FPII will remove it. You could also clay while doing the initial wash. I have never used FPII but my understanding is that it is pretty mild. If you swirls are pretty mild you should be good. Start with the least aggresive polish and if that is not working to your satisfaction use a more aggresive polish.
Have fun and let us know how the detail turned out.