As long as your 3-piece rims aren't rusted/pitted and worn so much that they won't stay together, they're pretty safe as far as such things go.
The rims that DOT outlawed were the two-piece rims that split in the center of the rim gutter...if these weren't put together right or became worn or rusty, the whole wheel could come apart and the tire come off the rim...
Get a reprint of an original factory shop manual: it will have detailed instructions on tire mounting.
I don't think the two-piece "widow-makers" came out until the early '50s.
The only "newer, safere style" would be a one-piece steel or aluminum rim for tubeless tires...I'm sure these are pricey...
