I'm doubtful about cleaner wax doing it, but it's worth a try.
Start with the easy stuff and only step up in agressiveness as much as you have to.
I would start with a good wash with plain ol' dishsoap. Ivory seems to be recommended the most, but that might just be a brand-saturation kinda thing.
That strips any wax, oil, grease, ect off of the paint. Then do the cleaner wax, which is just mildly abrasive.
If your buffing pads (handheld or those on a slow-speed orbital buffer) are getting really black from paint transfer (they'll also just get dirty- but that'll be a lighter color), your clearcoat is shot.
If they don't, but the scars are still there, another Ivory bath and claybar might be a good next step.
Then you're pretty much down to rubbing compounds and high speed polishing.