You will almost certainly need an Anti fatigue mat for stationary standing for long periods of time. It does not matter much how the soles of your shoes are, likely your issue is arch support, for which you will want insoles for your shoes. No shoe by default is going to be right for everyone and you probably have a High arch. the anti fatigue matting I can recommend as I used to work in a casino dealing table games. All our tables had anti fatigue mats and I never had an issue in that casino. Went to work at a different casino in the same shoes where they did not have anti fatigue mats and my feet were sore after the second hour long rotation on the table.
You may also like to have a 4 inch tall moveable step under your desk so that you can stand on one leg, and have your other foot up on the step just to steady you, when the leg on the floor gets tired switch to the other, this will help stimulate some motion as you will not be standing in a fixed location at all times. This is another technique used at the first casino I worked at where I did not have any issues.