As far as I know, P21S does not have any abrasives (according to the various polish charts - Todd Helme's is excellent if you haven't seen it) and therefore would not remove swirls, however light they may be.
What it will do, though, is fill the swirls and make it appear as though you have removed them. It can be thought of as a glaze, more than a polish (as you'll see, in the detailing world, any word can really mean anything.)
A good fine polish will remove the swirls, but since you don't have one, if you were to use M105 on a finishing pad it may be light enough to come out nicely. Of course, you would need to do a test spot but short of purchasing a fine polish, I don't know if you'll be able to remove them. You can fill them, though, if that would work until you acquire a good finishing polish.
Hope this helps! Happy detailing!