I think the wall thickness has been explained pretty well already. But I just had a few thoughts that I feel you should consider.
As far as I understand, this endeavour will be a “2.5D”-honeycomb, where you draw the hexagons in xy hundreds of times. (If not, don’t even think of printing this on a FDM machine!)
I have had to print similar honeycombs before, albeit with much larger hexagons (2.5cm sides) and smaller blocks. The biggest problem there was not even wall thickness, but very, very severe thermal warping. With PLA that is. Basically, the prints took so long, that the thin walls just melted into themselves and lifted from the bed, despite running only 60°C pure glass bed which had given me zero problems for hundreds of hours before.
My point is, do test prints before you embark on the full 200mm height.
Another point is the material. As I said, even PLA can give you trouble, most likely since the contact area with the bed is pretty small. That’s kind of the point of honeycomb, right? What I would suggest is some sort of composite material. In my experience, these have very, very, very low tendencies to warp. It does not necessarily have to be carbon fibre, even though I particularly like @Colorfabb’s XT-CF20. Wood filled material will be just as light “proof”, quite a bit cheaper and you don’t need to worry about hardened nozzles. For this application I would recommend FormFutura’s EasyWood.
