I've heard it is thought to have been some kind of speech impediment.
And as for DNA, isn't there a time limit, that after 5 or 10 years it corrupts and can't be used in lab analysis? If unexplained incorruption was found, the skeptics would claim that must prove the remains are of recent origin.
I'm not sure what DNA analysis would get you; maybe some sort of likelihood the body was that of a Jew. Carbon dating might get you the age to within half a century or less. That could prove it was St. Paul or at least a contemporary. But (speaking as an ex-Catholic) I can't see the Church allowing destructive testing on the possible relics of a saint.