Welcome to the Stovebolt Page. My personal experience has been 3 55-first and older "AD" 3/4-tons. They all had 15" split rim wheels. The 16" ones like your truck has were used into the 70's and 7.50-16 tires are still available. Try here
http://powerkingtires.com/Tires/Highway/Bias%20Light%20TruckSome auto tire shops don't/won't work on the 2-piece wheels but you should be able to find a truck or ag tire shop that does.
Really, if your original wheels are in good shape, not damaged, bent or rusted, they are plenty safe and not that hard to work on.
Try a search of these forums as 3/4-ton wheel and tire discussions pop up often.
Good luck with your 55.
Also find the wheel-tire tech tip on this site.
http://www.stovebolt.com/techtips/wheels/