Swirly marks in a guitar finish.

Is it a satin or gloss finish, and do you have photos that show the depth and scope of the swirls?

In the case of glosses ...

If they are shallow, ex. polishing swirls, they can often be taken out buffing by hand via nice automotive scratch removers available at a good auto parts store.

If they are deeper, I use micromesh fine abrasives prior to buffing.

If they are very deep, they can often be filled with CA glue and the fills leveled prior to the stuff above.

In the case of satin finish, you're better off leaving as is.

IMPORTANT: Corrective guitar finish measures on a cherished guitar are not necessarily recommended for the DIY'er's first stab at the task. Finish issues can be tricky and you can often create more damage than good if you don't know what you are doing .. and create problems that would require (in this case) refinishing to correct. If you are determined to fix it and do it yourself, go buy a cheap beater acoustic in similar cosmetic condition off a pawn shop wall or CL and practice on that first!