Yes, you would need to provide factory documentation on an optional tire. If there is a question from the Judging Team, the Captain will approach you. Best place to look first is in the owner's manual.
The Best way to deal with the fact that you cannot find the right size tire is to contact the VP of Judging.
There are owners who want to run radials when they are not showing, so they buy two sets of proper wheels.
Owners not able to find a correct replacement tire should send a letter to the VP Judging indicating the specific size of the correct tire and that at least two tire manufacturers have been contacted and the correct tire is not available. Tires one size larger or smaller are acceptable. A letter from the VP Judging is the ONLY AACA ACCEPTED documentation regarding a vehicles' substitute tires. Any letter issued by the VP Judging should be shown to the Team Captain at the time of vehicle judging. IT IS IMPERATIVE THAT THE TEAM CAPTAIN ASK FOR DOCUMENTATION FOR ANY TIRE THAT IS QUESTIONED BY THE CHASSIS JUDGE OR DOES NOT MEET THE FIRST YEAR OF MANUFACTURE GUIDELINES LISTED BELOW. Some manufacturers offered a radial tire – for specific vehicle(s) - as a factory authorized option to the standard issue ply tire. The use of red line radials on a vehicle should be accompanied with documentation. It is advisable to seek documentation from the vehicle 2-23 owner when a tire size or type is in question. This is especially so in cases of limited production, specialty vehicles, and foreign made vehicles..."
"b. RADIAL TIRES (e.g., 185R14, 175R13, etc.), Domestic Cars. (Factory documentation is required for any vehicle with radial tires prior to the years listed below.) Some domestic manufacturers offered these tires as early as 1967, such as Buick and Oldsmobile. It is possible that others may have offered them as well. BEFORE taking any deductions, the Team Captain will ask the owner for documentation. Note: European built vehicles can be much earlier. Japanese vehicles 1967, possibly earlier. c. LOW PROFILE METRIC RADIALS (e.g., P195/70R13, P195/70VR14). Domestic Cars as early as 1979. European cars 1969*, Japanese cars 1975*.