Given it was used as a test by Yon-Rogg to determine whether or not it was the real Danvers he was speaking to and the Skrull's inability to answer was enough for Yon-Rogg to shoot the Skrull, he would have to be pretty certain that the real Danvers would know (or at least believe) she had received Yon-Rogg's blood.
Additionally, Mar-Vell's engine was not necessarily anything to do with Kree technology. It was mentioned by a Skrull, iirc Thalos(?) that her powers exhibited the same energy signature as the engine, which would suggest that all the explosion gave her was Tesseract power, something that is unlikely to give Danvers Kree blood since the Tesseract's power pertains to space.