Need someone with '68/'69 A-body rad experience.....

I've run a few 60s 318 cars, and can't recall them having shrouds. Even ran a "big-bore" teener in a 65 Valiant wagon with no shroud.
I wonder if there is an underlying issue.
I understand that what you are contemplating will probably cure it tho, so perhaps it's moot to mention it. Be vigilant.