There are obviously pros and cons to this question.
I have 650-16 bias ply on my 49 and love them. Granted I don't drive freeways or above 50 mph. I had a 53 with 15" radials and I found them okay but no better than my bias ply. I did find it hard to park or turn the truck at low speeds.
There are again two schools of thought on putting radials on old rims. Some say they will cause damage, others say not. There is also talk of the front end set up having to be changed if one converts to radials, toe-in, etc.
Two friends of mine, one with a 58 Corvette and the other with a 67 Malibu, both converted to radials and both went back to bias ply.
I did consider going to radial tires (215-85R16) on the 49 because up here bias ply tires do not exist. No dealer wants to even talk about them. I bought a set of radials and the dealer was quite concerned about my narrow stock rims and the fact there was no safety bead on them. He said he would install them but would not warrant the tire nor would he accept responsibility if the tires came off the rims (!).
I checked with 2 more tire dealers and had the same experience. Incidentally my experience has been discussed in these Forums.
A lot of this Forum's members have put radial tires on stock 4" rims with success. However if you look at the profile or the sidewall bulge you can see that the rim is too narrow. The manufacturer's specifications call for a 5.5" rim width as a minimum for the above radials.
Again this is my opinion and experience and as mentioned above there are two sides to these question so you will probably get comments from others who disagree entirely.