I'm in the "don't worry about being one of the cool kids" group. I change one or two flats every year on the side of the road, along with the tubes/tires I change at home. I swallow my pride and always use tire levers. (I'm in awe of the guys who can remove/mount tires without levers, but it's beyond me and I've never had a problem using levers with sidewall failures.) On the side of the road, I use a CO2 inflator. Practice using one if necessary, but I've never had a problem with them. At home, you'll always have your floor pump. As far as using a mini pump on the side of the road, they require a fair amount of effort and upper body strength and even then it will take a few minutes to get a reasonable amount of air into the new tube. A frame pump works better, but I haven't had one of them on my bike in the last 30 years.

Good luck!