Since Paul never claims to have encountered the physically risen Jesus, and instead had merely experienced Jesus in a vision, a martyrdom would only suggest his conversion was genuine. It lends no credence whatsoever to the historicity of the resurrection.

Speaking of James, the brother of Jesus, Max claims that Josephus, higgisippis and Clement of Alexandria all attest to his martyrdom.
Josephus writes in Antiquities of the Jews,

Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrim of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned.