I assume you will be doing this by hand correct?
First, wash the finish, dry, then use a clay kit. The "Clay Magic" kits are very good and do not leave behind a lot of residue. After all the claying is done, wash & dry it again.
Get a bottle of Megs PPC (Premium Paint Cleaner) and use that to remove the swirls. Follow with Megs #9. Use high-quality terry towels to polish with, not some cheap ones or you'll end up with more than swirls! Only 100% USA Cotton! Look at the label!
If your swirls are that bad, you may need to step up to Megs DACP. Although meant for rotary/RO use, it can be done by hand application. You need several good high-quality terry towels to polish it with. It also has to break down, in that I mean the polish will be wet at first, then start to go to a powder stage. That shows that it has broken down and ready for wipe-off. Use it sparingly, as too much will end up in it being difficult when you try to remove it.
A quicker way is of course a PC.
Regards,
Deanski