What stone? IMO the patio tile will drive all choices and since it is so busy I would not do any stone accent anywhere next to it

I don't think stone is the answer here either. Can you post a shot of the patio from further back? If the pool is finished a shot of it as well.

When the new pool goes in there will be traverteen just beyond the stamped concrete patio posts. We were thinking on an ivroy color stone veneer wrap but just up arounbf 3 feet. Too much?

Instead of cladding the pillars and making them even wider, consider how you can make them much narrower and still have support or whether you can get rid of some altogether. It looks like you have a bench directly behind one - you want to open up the view of your new pool, not place obstacles in front of it.