The wheels you have at 4" wide were original for 48. Sometime later (49 or 50) GM went with 4.5 inch wide wheels. And then I think in 55, they were 5" wide. I have some of each size. The 5" wheels had only 3 hubcap clips instead of the 6 on the earlier (narrower) wheels. I don't think even 215/85R16 tires are supposed to be mounted on wheels narrower than about 5" but a lot of guys get away with them. Most tires of that size are light truck (as in modern light truck) and heavy load range, which will translate to a stiffer ride.
You might be able to track down some 4.5" wide original rims, and maybe trade your 4" rims to someone who's looking to be original-original with a 47 or 48.
Alternative - I found 6.50-16 tires from Simple Tire for less than $100 each.


Kevin
1951 Chevy 3100 work truck
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1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car)
Busting rust since the mid-60's
If you're smart enough to take it apart, you darn well better be smart enough to put it back together.