My vote is for cyclo polisher. it is the less aggressive unit. In the hands of someone that does not do this for a living it is less likely to mar or sratch the finish.

The term polish seems to be used interchangeably with wax or sealant. If I understand the O.P.

The Poter Cable machine is a crude sanding machine (basic workhorse) with a different backing pad.Lots of vibration, used one for years before switching to festool. That being said in the right hands it can do a great job.

 

The grey version was some of the easiest I've used. I had my griots out but it was equally easy by hand.

 

Since having my lower front bumper wrapped in SunTek, I called the manufactuer to ask about proper care. (fwiw, I also have white) There really should be a need to use a DA or any other polisher on the material since it's all scratch and swirl "proof." The challenge is to get is clean and here's what I found out.

1. can use Nanoskin or traditional automotive clay to remove contamination whenever necessary. After washing, place your hand inside of plastic sandwich bag and feel the paint, if it's gritty than it need to be clayed.
2. P21s TAW (it's actually an all purpose cleaner) which is TUV approved and won't harm the wrap or the paint to get the material clean & to remove any staining
3. Paint cleansers are fine to use by hand which are non abrasive polishes. Suggested products Ultima Prep Plus, P21s Paint Cleanser or Sonax Premium Class Paint Cleanser.
4. They suggested spray wax but I've had issues with OEM stone guards turning yellow. A colorless spray sealant is what I would recommend, something like Blackfire Crystal Seal or CarPro Reload. Note that I'm a huge fan of carnuaba waxes and I wouldn't use any of them because of the potential of clogging the porous wrap material and discoloring it over time.
5. These wrap materials are designed to require very little maintenance so less is more.
6. Like paint, remove stains and bird bombs with detail spray or waterless wash asap
7. Again, stay away from using a buffer, there really shouldn't be the need.