I'm not necessarily suggesting that they'd need to use diplomacy, but they could have somehow captured phasers or it turns out that Chapel was with Pike on Discovery (as at least the saucer of this ship was Crossfield class) and she knew where the Jeffries tubes were to get them where they needed to be. They could have told one of the Klingons that they'd had a medical emergency reported in the transporter room and they needed to get there fast. If they were playing the trauma from the Klingon war angle, I think all of the references are really too abstract for us as an audience to get that and I don't think the scene was quite good enough to give us a mystique.