Most automotive "polishing compound" I've used has been very, very aggresive. You have to be exceedingly careful in using it or you will cut right through the paint. Get a wax with a very, very mild abrasive in it and take your time.

Completely avoid the use of power polishing with a wheel unless you know how to use one (very judiciously).

One thing I've seen but never used, which I believe is a relatively new product for automotive paint finishes, is called "clay". Have you looked at those? I believe it is a mild abrasive in a media that allows hand application.

I've done a LOT of polishing of paint and clear costs in my hobbies. Then again, I actually enjoy the time I spend sanding. It's very tactile, like polishing. Go slowly at first and enjoy the hand labor. You can always do more but you can never put it back.