First, very few of these trucks have their original engines or other parts. Nobody really cares and I don't even think it affects the value in a negative way. Most people would rather have the 235 instead of the 216.
My truck has a 1951 engine and a 1941 radiator.
Anyway, I would not buy the cheapo aluminum radiator. I'd have your original repaired. How do you know it needs to be recored? It may just need to have some of the tubes soldered up.
In the overall scheme of things, how much is the recore job compared to other crap you spend money on? Spend the money to do it right and you'll forget about the expense as soon as you're driving the truck.
The radiator part number is embossed on the top tank. You can use the numbers to see if it actually is the original radiator. Even if it isn't, it will be a lot better than anything made today, I'm sure.