Voice assistants (VAs) are becoming a feature of our everyday life. Yet, the user experience (UX) is often limited, leading to underuse, disengagement, and abandonment. Co-designing interactions for VAs with potential end-users can be useful. Crowdsourcing this process online and anonymously may add value. However, most work has been done in the English-speaking West on dialogue data sets. We must be sensitive to cultural differences in language, social interactions, and attitudes towards technology. Our aims were to explore the value of co-designing VAs in the non-Western context of Japan and demonstrate the necessity of cultural sensitivity. We conducted an online elicitation study (N=135) where Americans (n=64) and Japanese people (n=71) imagined dialogues (N=282) and activities (N=73) with future VAs. We discuss the implications for coimagining interactions with future VAs, offer design guidelines for the Japanese and English-speaking US contexts, and suggest opportunities for cultural plurality in VA design and scholarship.