I don't understand why People are assuming that Mihawk is Imu's Son, I told you before that Double-Layered Eyes mean Two People are looking through them, it means Mihawk just like Imu & Hakuba, is also possessing that Body We see,
As for similar Sword-Style, it's no different than Brook's Assault Squad, it simply means that Imu & Mihawk are from same Ancient Group, this Chapter isn't trying to prove that Mihawk & Imu are Family, it's instead indirectly confirming that Mihawk is also One of 20 Founders,