The latin source word is much older than 1500s, but the question is whether they understand what it's about.

Both the 15th century "radiacion" and the latin "radiationem" are about emitting light and are synonymous with "to shine" or "to glow" (though without the heat connotation).

None of that conveys the sense of danger and fear of death that the modern word "radiation" means.

Kinda like how the word "plane" was in use in English in the 1600s and derives from the much older Latin word "planum", but if I'd tell some from 1600s England or from ancient Rome that I took a plane/planum to another country, they'd be utterly confused about what that means.

The word is the same (or at least very similar), but the concept is unknown.

So you need to find a concept that's similar to what you want to convey, and then use the fitting word.

For example, someone from the 1600s might understand the term "flying machine" (which was a well-known word in use in research and "science fiction" at that time).