I have a trailer of similar age, even though mine is a little smaller.
I think the idea is to do a very thorough inspection of the wheels with the tires removed, before you can make an intelligent decision.
If the wheels show no dents or cracks, and look rust free, then it might not be a problem to go to D-rated (8ply) tires.
Also, make sure the wheels are original equipment or equivalent, not mismatched or of lesser quality.
I had to replace my wheels because they were very rusty, and the new tires would not hold air reliably. When I removed the tires I saw a lot of rust inside the wheel, along the welds and in the wheel bolt area. My old wheels would have eventually caused a problem, from the looks of them.
If in doubt, just buy new wheels and tires, and keep the very best one of the old ones for a spare, perhaps.