No requirement to inform in MO and CCW will come up with the registered owner of the license plates.
I haven't been pulled over in the near decade that I've been carrying. But in most situations and states, required or not, I have decided I will inform just as a courtesy. Depending on the situation and how I'm carrying, verbalizing may not be the best path. Might just hand the cop my CCW with my DL & insurance. I've had the misfortune of interacting with some of the not good cops over the years too. Those are the exception situations where I would not say anything beyond what is strictly required. But then long before I carried I learned to put it in park and take my foot off the brake, keep my hands on the steering wheel and if night, turn on the dome light all before the cop gets out of the car. I met more than a few cops in my younger, more speedy days, and once I started doing that when pulled over I found that more often than not I got a warning. I like to think it was just a returned kindness for my helping him/her feel a bit more at ease.
As far as reaching for stuff, since I started carrying I have changed how I carry my IDs. I almost always carry right hip so now I carry my IDs & insurance card in a small credit card wallet in my left front pocket instead of my pre-carry days of in a regular wallet in my right rear pocket. That way I can keep my right hand on the steering wheel or where ever appropriate if on the street and only reach with my left, away from my sidearm, to provide requested info.