I appreciate what you are trying to accomplish and there may be options but I disagree that a shifter kart is even remotely a good option for someone that has safety concerns and is not an experienced autocrosser. I spent 5 years autocrossing before I got into karting (been karting 7 years) and decided a few years ago to take my shifter autocrossing for a day just to have some fun. While I had fun, it was extremely rough on the kart and was somewhat terrifying.
The autocross course was at a “nice” parking lot but even the smallest mismatches in concrete not only damaged the bottom of my chassis but I also had to constantly catch and correct as the kart bottomed out. Manhole covers and drain grates suddenly became terrifying as in a car you are worried about light poles… well… in a kart there are a lot more things to worry about avoiding. At the same time this is all happening at a pace that is dramatically faster than any single car out there (I was 3.5 seconds faster than that fastest mod car out there and probably 6-8 seconds faster than a street legal Miata). I honestly don’t know if I could’ve caught the kart in time to not hit something if I hit a slick spot or a hub came off or some other failure (keep in mind I consider myself an experienced autocrosser AND karter).
I’m also reminded of an incident a few years ago where a young girl died at an autocross because of some failure on her kart. I don’t recall specifically what the failure was but I’ve had throttle’s stick on me (the cable unraveled in the sleeve) and I’ve seen people with brake failures.
I love karting and push this sport at any chance I get but in this case I think you should steer away from it. My wife and I both autocrossed and she was never comfortable enough to drive the Porsche that I raced but she still had a ball racing her VW Beetle! :)