https://en.wikipedia.org/wiki/Blood_type#History
and some information about blood typing was famous enough to get the medicine Nobel in 1930
https://en.wikipedia.org/wiki/Blood_transfusion#20th_century
So maybe you could try to draw an analogy and say "as with blood typing, many more hereditary structures and features of tissues will be discovered at the chemical and microscopic levels, collectively sufficient to perform definitive studies of hereditary relationships on the basis of tissue samples".
It might be credible at that level, even though that description is a little bit misleading (because you're not actually using random sets of phenotypic features, but rather the actual underlying genetic data). But I imagine the coroner could at least believe that there are microscopic features that are heritable that would one day be subject to more and more informative analysis. And blood types could be a good prototype of that.
I'm not sure the coroner would find it that intuitive that genetic information is carried or expressed in hair, though!
It wasn't until 1952 that DNA was confirmed to be the carrier of hereditary information[1]. Would an average (educated) person in 1948 even suspect that such a thing might be possible, or would it sound like crazy science fiction?
I wonder what astounding forensic techniques will emerge 50 years from now that might be applied to solve present day mysteries. Probing people's brains—living or dead—to directly extract memories? What else?
[1] https://en.wikipedia.org/wiki/Hershey%E2%80%93Chase_experime...