Unfortunately that is one of the problems with double or multiple layers of panels hiding hard to reach cavities behind. They are all over these cars and bodies weren't dipped back then. Your concern is real, but do a good inspection of door sills, inside fender wells against the outer body panels, along the frame where panels have been overlapped and spot welded, the underbody, etc. It means taking some interior panels, sill covers, etc off. I believe Eastwood (and others) make products with a long, skinny spray nozzle to get into areas like that, if it's not too late.
I would hit it with a wire brush and spray on some rust converter, call it a day. There is rust lurking in many areas, so unless you want a years long process of deconstruction and then reconstruction after 10's of thousand of dollars, best bet is to wait and see what pops up and fix it as soon as it shows. Oh and park your car inside a garage, keeping it out of the elements is the best thing you can do.