I don't know the answer about which is 'correct', but I've seen both.
Last year when I re-cored Lurch's radiator, I combined a few parts from 3 different radiators. Two used the surround brackets and one had the brackets soldered to the core.
Since Lurch's old radiator used the surround brackets, that's what I went with. I suspect that your radiator with the soldered brackets will work just fine, but you don't need the surround brackets for that one.
Does it have a bracket on the bottom to bolt the radiator to the chassis front cross member? If not, you might need to fabricate something that is in the same vein as the bottom surround bracket.
BTW, my re-core job with a new three-row copper regular core + labor came to around $750 at a local old-school radiator shop.
New honey comb cores started at $3000! This was in May 2022.
Dean
