The twist-lock end on the side of your camper is a standard configuration and is available from a few different well-known brands and some unknown offshore brands. Don't know about Conntek or Furrion, but on the Park Power/Marinco cord, you can get a collar that threads onto the power inlet or is 1/8 turn. We have the 1/8 turn and have had the threaded one in the past. I like the 1/8 turn much better.
The cords can be found on the internet from RV parts vendors or ebay or Amazon. Pays to shop around. You can also find them on CL sometimes. Don't buy a used one if the plug blades are pitted and dirty.
It's not a good idea to run an AC unit on 15 amps, even if nothing else is running. AC units draw around 12-15 amps depending on make & model. A converter will draw at least a few amps. Some will claim it's not an issue, but if you want to shorten the life of an AC unit or cause a cord's plug or connector to melt down, you can try it and find out what happens. New AC units are not cheap.
FWIW, when buying shore power cords or adapters, look to see if they're UL listed. If not, the quality of internal parts is unknown and could cause a poor connection. Unlike just about everything else electrical in this world, cords & adapters aren't required to be UL listed.
Gil & Deb & Dougal the Springer Spaniel