While social robots have demonstrated effectiveness in supporting students' intercultural competence development, it is unclear how they can effectively be adopted for integrated use in K-12 schools. We conducted two phases of design workshops with teachers, where they co-designed robot-mediated intercultural activities while considering student needs and school integration concerns. Using thematic analysis, we identify appropriate scenarios and roles for classroom robots, explore how robots could complement rather than replace teachers, and consider how to address ethical and compliance considerations. Our findings provide practical design guidelines for the HRI community to develop social robots that can effectively support intercultural education in K-12 schools.