https://www.gunstocarry.com/gun-laws-state/kansas-gun-laws/#recip
Looks like your permit is fine. Don't need to say anything to the officer if pulled over. I have always just handed my ccw permit with my DL and they have just asked where it was. Nothing beyond that. Happened one day as a buddy and I left the range. That guy asked what we had....we chuckled and then proceeded to tell him about the arsenal that happened to be in the car. My buddy, who was driving, got a warning lol
KS is about as good as it gets with regards to concealed carry. You will want to stay away from government buildings and sporting events. Signs aren't enforceable, but if you are made and asked to leave then you need to GTFO or you will have a problem. You can go into restaurants and bars without issue. We have castle doctrine